CiteSl

"At the very least you should try all that are built into the computer algebra systems that you already have, together with all of the web-based tools (…, the Online Encyclopedia of Integer Sequences, …) because that is so easy to do." [David R. Stoutemyer, 2021]

"This continued fraction ought to be classical, but the first mention of which I am aware is a 2006 contribution to the OEIS by an amateur mathematician, Paul D. Hanna, who found it empirically; it was proven a few years later by Josuat-Vergès [49] by a combinatorial method (which also yields a q-generalization)." [Alan D. Sokal, 2018]

"This work was immeasurably facilitated by the On-Line Encyclopedia of Integer Sequences [16]. I warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it." [Alan D. Sokal, 2019]

"Using the On-Line Encyclopedia of Integer Sequences (OEIS), we have seen that quite different sequences can have the same binary operators. We have also found integer sequences not given in OEIS and that need to be studied." [Amelia Carolina Sparavigna, 2019]

"Neither this paper nor my PhD thesis would have happened if it weren't for the OEIS.'" [Christopher Stokes, commenting on Stokes (2022)]

"There is a Web Page: <https://oeis.org/> by N.J.A. Sloane. It tells, from typing the first few terms of a sequence, whether that sequence has occurred somewhere else in Mathematics. Postgraduate student Daniel Steffen traced this down and found, to our surprise, that the sequence was related to the tangent function tan x. Ryan and Tam searched out what was known about this connection and discovered some apparently new results. We all found this a lot of fun and I hope you will too." [Ross Street, 2015]

About this page

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References

Paul B. Slater, Eigenvalues, Separability and Absolute Separability of Two-Qubit States (2008); arXiv:0805.0267
Paul B. Slater, Formulas for Generalized Two-Qubit Separability Probabilities, arXiv:1609.08561 2016.
Paul B. Slater, Hypergeometric/Difference-Equation-Based Separability Probability Formulas and Their Asymptotics for Generalized Two-Qubit States Endowed with Random Induced Measure, preprint arXiv:1504.04555, 2015. (A004523, A232007)
Peter J. Slater, It Is All Labeling, In: Gera R., Hedetniemi S., Larson C. (eds) Graph Theory. Problem Books in Mathematics. Springer, 2016, doi:10.1007/978-3-319-31940-7_6
Michael C. Slattery, Groups with at most twelve subgroups, arXiv preprint arXiv:1607.01834, 2016
Richard M. Slevinsky, On the use of Hahn's asymptotic formula and stabilized recurrence for a fast, simple, and stable Chebyshev-Jacobi transform, arXiv preprint arXiv:1602.02618, 2016
Arkadii Slinko, Algebra for Applications: Cryptography, Secret Sharing, Error-Correcting, Fingerprinting, Compression, Springer 2015.
N. J. A. Sloane, A handbook of integer sequences, Academic Press (1973)
N. J. A. Sloane, An on-line version of "The Encylopedia of Integer Sequences", Electron. J. Comb. 1 (1994) 179-183
N. J. A. Sloane, The Sphere Packing Problem, Proceedings Internat. Congress Math. Berlin 1998, Documenta Mathematika, III (1998), pp. 387-396. (pdf)
N. J. A. Sloane, My Favorite Integer Sequences, in Sequences and their Applications (Proceedings of SETA '98), C. Ding, T. Helleseth and H. Niederreiter (editors), Springer-Verlag, London, 1999, pp. 103-130.
N. J. A. Sloane, On Single-Deletion Correcting Codes, in K. T. Arasu and A. Seress, eds., Codes and Designs, Ohio State University, May 2000 (Ray-Chaudhuri Festschrift), Walter de Gruyter, Berlin, 2002, pp. 273-291.
N. J. A. Sloane, The Sphere-Packing Problem (2002), arXiv:math/0207256.
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences (2003), arXiv:math/0312448; Notices Amer. Math. Soc., 50 (September 2003), pp. 912-915.
N. J. A. Sloane, arXiv:0912.2394 Seven Staggering Sequences.
N. J. A. Sloane, Gleason's theorem on self-dual codes and its generalizations (talk given at Conference on Algebraic Combinatorics in honor of Eiichi Bannai, Sendai, Japan, June 2006).
N. J. A. Sloane, Eight Hateful Sequences, arXiv:0805.2128 (2008). See also Ch. 1, Barrycades and Septoku: Papers in Honor of Martin Gardner and Tom Rodgers, AMS/MAA Spectrum (2020) Vol. 100, 4-9. (A000203, A001008, A002805, A003001, A006960, A033865, A051003, A064413, A090822, A130316, A130838, A131286, A131287, A131744, A131745, A131746, A133242, A133500, A133816, A133817, A134204, A135385, A135473, A135475, A138563)
N. J. A. Sloane, 2178 And All That, PDF and Fibonacci Q. 52 (2) (2014) 99-120
N. J. A. Sloane, The on-line encyclopedia of integer sequences, Ann. Math. Inform. 41 (2013) 219-234
N. J. A. Sloane, 2178 And All That, Video of talk given in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Oct. 10 2013: <a href="https://vimeo.com/76725343">Part 1</a>, <a href="https://vimeo.com/77255410">Part 2</a>.
N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015
N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, Notices, Amer. Math. Soc., 65 (No. 9, Oct. 2018), 1062-1074 doi:10.1090/noti1734. Reprinted in "The Best Writing on Mathematics 2019", ed. M. Pitici, Princeton Univ. Press, 2019, pp. 90-119 and colored illustrations following page 80.
N. J. A. Sloane, The OEIS: A Fingerprint File for Mathematics, arXiv:2105.05111 [math.HO], 2021. (A003987, A007318, A098550)
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023. doi:10.1007/s00283-023-10266-6, The Math. Intell. (2023) (A000001, A000002, A000004, A000010, A000040, A000043, A000081, A000108, A000124, A000203, A000435, A000602, A000787, A000796, A001006, A001011, A001034, A001116, A001203, A001477, A001855, A002410, A002921, A003600, A003991, A005132, A006064, A006561, A006577, A007318, A007678, A008892, A011554, A027641, A027642, A030430, A036910, A051070, A051602, A055682, A064413, A098007, A098550, A107357, A110312, A121053, A131744, A250001, A255011, A257479, A291789, A292108, A307720, A331449, A331763, A331766, A334699, A336957, A337663, A341578, A342585, A348453, A354169, A355798)
N. J. A. Sloane and Parthasarathy Nambi, Integer Sequences Related to Chemistry, pdf, Poster presented at the Amer. Chem. Soc. National Meeting, San Francisco, Fall 2006.
N. J. A. Sloane and J. A. Sellers, arXiv:math.CO/0312418 On non-squashing partitions], Discrete Math., 294 (2005), no. 3, 259-274.
N. J. A. Sloane and Thomas Wieder, arXiv:math.CO/0307064 The Number of Hierarchical Orderings, arXiv:math.CO/0307064, also doi:10.1007/s11083-004-9460-9 Orderings, Order 21 (2004), no. 1, 83-89.
Slomczynska, Katarzyna Free spectra of linear equivalential algebras. J. Symbolic Logic 70 (2005), no. 4, 1341-1358.
Michael Small, C.K. Tse, David M. Walker, Super-spreaders and the rate of transmission of the SARS virus, Physica D: Nonlinear Phenomena, Volume 215, Issue 2, 15 March 2006, Pages 146-158.
F. Smarandache, arXiv:math.GM/0010137 Another Set of Sequences, Sub-Sequences and Sequences of Sequences, Partially published in "Only Problems, Not Solutions!", by Florentin Smarandache, Xiquan Publ. Hse., Phoenix, 1991.
F. Smarandache, arXiv:math.GM/0010132 Considerations on New Functions in Number Theory, Partially inlcuded in the book "Noi Functii in Teoria Numerelor", by Florentin Smarandache, University of Kishinev Press, 120 p., 1999.
F. Smarandache, arXiv:math.GM/0010125 A Set of Sequences in Number Theory], Presented to the Pedagogical High School Student Conference in Craiova, 1972. "Collected Papers", Vol. II, book by Florentin Smarandache, University of Kishinev Press, Kishinev, 200 p., 1997.
F. Smarandache, arXiv:math.GM/0010151 G Add-On, Digital, Sieve, General Periodical and Non-Arithmetic Sequences.
Florentin Smarandache, Numerology (2000), arXiv:math.GM/0010132.
Florentin Smarandache, Sequences of Numbers Involved in Unsolved Problems (2006), arXiv:math.GM/0604019.
F. Smarandache, Generalization and alternatives of Kaprekar's routine, arXiv:1005.3235
Florentin Smarandache, Jean Dezert, An Introduction to the DSm Theory for the Combination of Paradoxical, Uncertain and Imprecise Sources of Information (2006), arXiv:cs/0608002.
Florentin Smarandache, Jean Dezert, The Combination of Paradoxical, Uncertain and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference, arXiv:cs/0412091 (2004)
SMBC (Saturday Morning Breakfast Cereal), The OEIS was the subject of the cartoon for Apr 09, 2022: https://www.smbc-comics.com/comic/oeis
Rasa Smidtaite and Minvydas Ragulskis, Commentary: Multidimensional discrete chaotic maps, Front. Phys. (2022) Vol. 10, 862376. doi:10.3389/fphy.2022.862376 (A061196)
Yotam Smilansky, Yaar Solomon, Multiscale Substitution Tilings, arXiv:2003.11735 [math.DS], 2020. (A328074)
David M. Smith, Geoffrey Smith, Tight Bounds on Information Leakage from Repeated Independent Runs, 2017 IEEE 30th Computer Security Foundations Symposium (CSF). doi:10.1109/CSF.2017.18
Hanson Smith, Ramification in the Division Fields of Elliptic Curves and an Application to Sporadic Points on Modular Curves, arXiv:1808.04809 [hep-th], 2018. (A085548)
Jason P. Smith, A Formula for the Mobius function of the Permutation Poset Based on a Topological Decomposition, arXiv preprint arXiv:1506.04406, 2015
K. W. Smith, KWSnet Mathematics Index, 2015; http://www.kwsnet.com/science-mathematics.html
Barry R. Smith, Reducing quadratic forms by kneading sequences, J. Int. Seq. 17 (2014) 14.11.8.
Hanson Smith, Ramification in Division Fields and Sporadic Points on Modular Curves, U. Conn. (2020). PDF (A085548)
Smith, Jason P. doi:10.1016/j.aam.2017.06.002 A formula for the Möbius function of the permutation poset based on a topological decomposition, Adv. Appl. Math. 91, 98-114 (2017).
Jason P. Smith, The poset of graphs ordered by induced containment, arXiv:1806.01821 [math.CO], 2018. (A088617)
R. Smith and V. Vatter, A stack and a pop stack in series, arXiv preprint arXiv:1303.1395, 2013
V. N. Smith and L. Shapiro, Catalan numbers, Pascal's triangle and mutators, Congressus Numerant., 205 (2010), 187-197.
Barbara Smoleń, Roman Wituła, Two-parametric quasi-Fibonacci numbers, Silesian J. Pure Appl. Math. (2017), Vol. 7, Is. 1, pp. 99-121. PDF (A000045, A001519, A001906, A014445, A015448, A020699, A028495, A030191, A052975, A074872, A081567, A081568, A081569, A081571, A081574, A094831, A096976, A099453, A120757, A122100, A123941, A124292, A147704, A163073, A163306, A181879, A188168)
Nicolas Allen Smoot, Computer algebra with the fifth operation: applications of modular functions to partition congruences, Ph. D. Thesis, Johannes Kepler Univ., Linz (Austria 2022), 33. PDF (A001617)
C. Smyth, The terms in Lucas sequences divisible by their indices, J. Int. Seq. 13 (2010) 10.2.4
Snellman, Jan, Standard paths in another composition poset. Electron. J. Combin. 11 (2004), no. 1, Research Paper 76, 8 pp.
Jan Snellman, Digraphs with a fixed number of edges and vertices, having a maximal number of walks of length 2 (2008); arXiv:0804.4655
Jan Snellman and Michael Paulsen, "Enumeration of Concave Integer Partitions", J. Integer Sequences, Volume 7, 2004, Article 04.1.3.
Marie A. Snipes, LA Ward, Harmonic measure distributions of planar domains: a survey, The Journal of Analysis, December 2016, Volume 24, Issue 2, pp 293–330.
Aaron Snook, Augmented Integer Linear Recurrences, http://www.cs.cmu.edu/afs/cs/user/mjs/ftp/thesis-program/2012/theses/snook.pdf, 2012.
D. R. Snow, Problems and Remarks, 18th International Symposium on Functional Equations, 1980, Remark 18. (ps, pdf)
Andrew Snowden, Measures for the colored circle, arXiv:2302.08699 [math.CO], 2023. (A127670)
Andrew Snowden, On the representation theory of the symmetry group of the Cantor set, arXiv:2308.06648 [math.RT], 2023. (A131288)
Sónia A. Soares, Hybrid acoustic model for sound propagation in a street canyon, Eindhoven University of Technology (Netherlands, 2020). PDF
E. V. K. Sobolev, A survey of the cell-growth problem and some its variations, preprint, Mar. 2001.
Bartosz Sobolewski and Lukas Spiegelhofer, arXiv:2309.00142 Block occurrences in the binary expansion, arXiv:2309.00142 [math.NT], 2023. (A014081)
Joram Soch, Expressing the Indefinite Integral of the Standard Normal Probability Density Function, arXiv preprint arXiv:1512.04858, 2015
Joram Soch, Linear Algebraic Number Theory, Part I: Foundations, arXiv:1709.05959 [math.GM], 2017.
Edwin Soedarmadji, Latin hypercubes and MDS codes, Discrete Mathematics, Volume 306, Issue 12, 28 June 2006, Pages 1232-1239.
Anthony Sofo, Fibonacci and Some of His Relations
Anthony Sofo, A family of definite integrals, Scientia, Series A: Math. Sci. (2021) Vol. 31, 61–74. PDF (A000364)
Takehide Soh, Packing Consequtive Squares into a Sqaure (sic), Kobe University (Japan, 2019). PDF (A005842)
A. D. Sokal, The leading root of the partial theta function, arXiv:1106.1003, 2011, and Adv. Math. 229, No. 5, 2603-2621 (2012).
Alan D. Sokal, The Euler and Springer numbers as moment sequences, arXiv:1804.04498 [math.CO], 2018. (A000111, A000464, A001586, A085734, A088874, A098906) "This continued fraction ought to be classical, but the first mention of which I am aware is a 2006 contribution to the OEIS by an amateur mathematician, Paul D. Hanna, who found it empirically; it was proven a few years later by Josuat-Vergès [49] by a combinatorial method (which also yields a q-generalization)."
Alan D. Sokal, Vertically constrained Motzkin-like paths inspired by bobbin lace, arXiv:1804.08919 [math.CO], 2018. (A260492)
Alan D. Sokal, A remark on the enumeration of rooted labeled trees, arXiv:1910.14519 [math.CO], Oct. 2019. Also Discrete Math., 341 (2020), #111865. (Sequences A071207, A232006.) [This work was immeasurably facilitated by the On-Line Encyclopedia of Integer Sequences. I warmly thank Neil Sloane for founding this indispensable resource, and the hundreds of volunteers for helping to maintain and expand it.]
Alan D. Sokal, Multiple orthogonal polynomials, d-orthogonal polynomials, production matrices, and branched continued fractions, arXiv:2204.11528 [math.CA], 2022.
Alpha Soko, James Makungu, Soliton Distribution in the Ball and Box Cellular Automation Model, American Journal of Mathematical and Computer Modelling (2019) Vol. 4, Issue 1, 27-30. doi:10.11648/j.ajmcm.20190401.14
Patrick Solé, The covering radius of permutation designs, arXiv:2108.04275 [math.CO], 2021. (cited: recontres numbers)
Patrick Sole and Michel Planat, THE ROBIN INEQUALITY FOR 7-FREE INTEGERS, INTEGERS, 2011, #A65; http://www.emis.de/journals/INTEGERS/papers/l65/l65.pdf
Fernando Soler-Toscano and Hector Zenil, A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences, arXiv:1504.06240 [cs.IT], 2017.
Allan I. Solomon, Gerard Duchamp, Pawel Blasiak et al., Normal Order: Combinatorial Graphs (2004), arXiv:quant-ph/0402082.
A. I. Solomon, C.-L. Ho and G. H. E. Duchamp, Degrees of entanglement for multipartite systems, Arxiv preprint arXiv:1205.4958, 2012
N. Solomon, S. Solomon, A natural extesion of Catalan numbers, JIS 11 (2008) 08.3.5.
Liam Solus, Simplices for Numeral Systems, arXiv:1706.00480 [math.CO], 2017.
Liam Solus, Local h*-Polynomials of Some Weighted Projective Spaces, arXiv:1807.08223 [math.CO], 2018. (A002301)
Steven E. Sommars and Tim Sommars, "The Number of Triangles Formed by Intersecting Diagonals of a Regular Polygon", J. Integer Sequences, Volume 1, 1998, Article 98.1.5.
Grace M. Sommers, Michael J. Gullans, and David A. Huse, Self-dual quasiperiodic percolation, arXiv:2206.11290 [cond-mat.stat-mech], 2022.
Michael Somos, A Multisection of q-Series, http://cis.csuohio.edu/~somos/multiq.pdf (A007325, A108483, A058531)
Michael Somos, A Remarkable eta-product Identity, http://cis.csuohio.edu/~somos/retaprod.html (A143751, A058728)
Sai Teja Somu, Andrzej Kukla, and Duc Van Khanh Tran, Some Results on Zumkeller Numbers, arXiv:2310.14149 [math.NT], 2023. (A005153)
Jonathan Sondow, New Vacca-Type Rational Series for Euler's Constant and Its "Alternating" Analog ln(4/Pi) (2005), arXiv:math.NT/0508042.
Sondow, Jonathan, A geometric proof that e is irrational and a new measure of its irrationality. Amer. Math. Monthly 113 (2006), no. 7, 637-641.
Jonathan Sondow, Which Partial Sums of the Taylor Series for e are Convergents to e? (and a Link to the Primes 2, 5, 13, 37, 463, ...) with an Appendix by Kyle Schalm (2007), arXiv:0709.0671.
Jonathan Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly, 116 (2009), 630-635.
Sondow, Jonathan; and Hadjicostas, Petros, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant. J. Math. Anal. Appl. 332 (2007), no. 1, 292-314.
J. Sondow and K. MacMillan, Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation, Amer. Math. Monthly, 124 (2017)232-240. doi:10.4169/amer.math.monthly.124.3.232
J. Sondow, J. W. Nicholson and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, Arxiv preprint arXiv:1105.2249, 2011. J. Integer Seq. 14 (2011) Article 11.6.2.
J. Sondow, E. Tsukerman, The p-adic Order of Power Sums, the Erdos-Moser Equation, and Bernoulli Numbers, arXiv preprint arXiv:1401.0322, 2014.
Nikki Sonenberg, Peter G. Taylor, Networks of interacting stochastic fluid models with infinite and finite buffers, Queueing Systems (2019) Vol. 92, Issue 3–4, 293–322. doi:10.1007/s11134-019-09619-w
Chunwei Song and Bowen Yao, On Combinatorial Rectangles with Minimum ∞-Discrepancy, arXiv:1909.05648 [math.CO], 2019. See also Enumerative Combinatorics and Applications (2021) Vol. 1, No. 1, Art. #S2R7. (A002896)
H.-Y. Song and J. B. Lee, On (n,k)-sequences, Discrete Appl. Math. 105, No.1-3, 183-192 (2000).
Eric Sopena, i-Mark: A new subtraction division game, arXiv:1509.04199, 2015
Henrik Kragh Sørensen, “The End of Proof”? The Integration of Different Mathematical Cultures as Experimental Mathematics Comes of Age, in Mathematical Cultures, pp 139-160 (2016); doi:10.1007/978-3-319-28582-5_9
J. Sorenson, J. Webster, Strong pseudoprimes to twelve prime bases, arXiv:1509.00864. See first page.
Jonathan P. Sorenson, Jonathan Webster, Two Algorithms to Find Primes in Pattern, arXiv:1807.08777 [math.NT], 2018. (A005602, A007508, A050258)
Øystein Sørensen, Marta Crispino, Qinghua Liu, Valeria Vitelli, BayesMallows: An R Package for the Bayesian Mallows Model, arXiv:1902.08432 [stat.CO], 2019.
Brianna Sorenson, Jonathan P Sorenson, Jonathan Webster, An Algorithm and Estimates for the Erdős-Selfridge Function (work in progress), arXiv:1907.08559 [math.NT], 2019. (A003458)
José Ezequiel Soto Sánchez, Asla Medeiros e Sá, Luiz Henrique de Figueiredo, Acquiring periodic tilings of regular polygons from images, The Visual Computer (2019) Vol. 35, Issue 6–8, 899–907. doi:10.1007/s00371-019-01665-y (A299780)
José Ezequiel Soto Sánchez, Tim Weyrich, Asla Medeiros e Sá, and Luiz Henrique de Figueiredo, An integer representation for periodic tilings of the plane by regular polygons, Computers & Graphics (2021) Vol. 95, 69-80. doi:10.1016/j.cag.2021.01.007
Jakub Souček, Ondrej Janíčko, Reverse Fibonacci sequence and its description, (2019). PDF (A057084)
Soulé, Christophe (13 Feb 2008). “Le triangle de Pascal et ses propriétés”. https://vimeo.com/100212123.
Richard Southwell and Jianwei Huang, Complex Networks from Simple Rewrite Systems, Arxiv preprint arXiv:1205.0596, 2012.
Jeremiah T. Southwick, Two Inquiries Related to the Digits of Prime Numbers, Ph. D. Dissertation, University of South Carolina (2020). Abstract (A050249, A076336, A125001)
C. A. Souza-Filho, A. F. Macedo-Junior, A. M. S. Macedo, A hypergeometric generating function approach to charge counting statistics in ballistic chaotic cavities, J. Phys. A: Math. Theor. 47 (2014); 105102 doi:10.1088/1751-8113/47/10/105102.
Yüksel Soykan, Gaussian Generalized Tetranacci Numbers, arXiv:1902.03936 [math.NT], 2019. (A000078, A073817)
Yüksel Soykan, Tetranacci and Tetranacci-Lucas Quaternions, arXiv:1902.05868 [math.RA], 2019. (A000078, A073817)
Yüksel Soykan, On Generalized Pentanacci and Gaussian Generalized Pentanacci Numbers, Preprints (2019). doi:10.20944/preprints201906.0110.v1 (A001591)
Yüksel Soykan, Matrix Sequences of Tetranacci and Tetranacci-Lucas Numbers, Zonguldak Bülent Ecevit University (Zonguldak, Turkey), Preprints (2019), 2019070205. doi:10.20944/preprints201907.0205.v1 (A000078, A073817)
Yüksel Soykan, On A Generalized Pentanacci Sequence, Asian Research Journal of Mathematics (2019) Vol. 14, No. 3, 1-9. doi:10.9734/ARJOM/2019/v14i330129 (A001591, A074048)
Yüksel Soykan, On Generalized Third-Order Pell Numbers, Asian Journal of Advanced Research and Reports (2019) Vol. 6, No. 1, Article No. AJARR.51635, 1-18. doi:10.9734/AJARR/2019/v6i130144 (A000129, A077939, A077997, A276225)
Yüksel Soykan, Summing Formulas For Generalized Tribonacci Numbers, arXiv:1910.03490 [math.GM], 2019. (A000073, A000931, A001608, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A078712, A128587, A159284, A176971, A226308, A276225, A276228)
Yüksel Soykan, On Summing Formulas For Generalized Fibonacci and Gaussian Generalized Fibonacci Numbers, Advances in Research (2019) Vol. 20, No. 2, 1-15, Article AIR.51824. doi:10.9734/AIR/2019/v20i230154 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, A Study of Generalized Fourth-Order Pell Sequences, Journal of Scientific Research & Reports (2019) Vol. 25, No. 1, 1-18, Article No. JSRR.52074. doi:10.9734/JSRR/2019/v25i1-230177 (A103142, A190139, A331413)
Yüksel Soykan, On Hyperbolic Numbers With Generalized Fibonacci Numbers Components, Zonguldak Bülent Ecevit University (Turkey, 2019). doi:10.13140/RG.2.2.19903.87207 (A000032, A000045)
Yüksel Soykan, Summation Formulas for Generalized Tetranacci Numbers, Asian Journal of Advanced Research and Reports (2019) Vol. 7, No. 2, Article No. AJARR.52434, 1-12. doi:10.9734/AJARR/2019/v7i230170 (A000078, A073817, A103142, A226309)
Yüksel Soykan, Sum Formulas for Generalized Fifth-Order Linear Recurrence Sequences, Journal of Advances in Mathematics and Computer Science (2019) Vol. 34, No. 5, 1-14. doi:10.9734/JAMCS/2019/v34i530224 (A001591, A074048, A141488, A226310, A226311)
Yüksel Soykan, On generalized sixth-order Pell sequences, Journal of Scientific Perspectives (2020) Vol. 4, No. 1, 49-70. doi:10.26900/jsp.4.005 (A000129)
Yüksel Soykan, Generalized Fibonacci Numbers: Sum Formulas, Journal of Advances in Mathematics and Computer Science (2020) Vol. 35, No. 1, 89-104. doi:10.9734/jamcs/2020/v35i130241 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, Closed Formulas for the Sums of Squares of Generalized Fibonacci Numbers, Asian Journal of Advanced Research and Reports (2020) Vol. 9, No. 1, 23-39, Article no. AJARR.55441. doi:10.9734/AJARR/2020/v9i130212 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, Generalized Tribonacci Numbers: Summing Formulas, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 7, No. 3, 57–76. (A000073, A000931, A001608, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A078712, A128587, A159284, A176971, A226308, A276225, A276228)
Yüksel Soykan, On Generalized Narayana Numbers, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 7, No. 3, 43-56. (A000930, A001263, A001609, A078012)
Yüksel Soykan, On Generalized Grahaml Numbers, Journal of Advances in Mathematics and Computer Science (2020) Vol. 35, No. 2: 42-57, Article no. JAMCS.55255. doi:10.9734/JAMCS/2020/v35i230248 (A335718, A335719, A335720)
Yüksel Soykan, On Generalized 2-primes Numbers, Asian Journal of Advanced Research and Reports, (2020) Vol. 9, Issue 2, 34-53. doi:10.9734/ajarr/2020/v9i230217
Yüksel Soykan, A Study On Sums of Cubes of Generalized Fibonacci Numbers: Closed Formulas of Sum_{k=0..n} x^k W_k³ and Sum_{k=1..n} x^k W_−k³, Preprints (2020), 2020040437. doi:10.20944/preprints202004.0437.v1 (A000032, A000045, A000129, A001405, A002203, A014551)
Yüksel Soykan, On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Sum_{k=0..n} x^k W_k², Archives of Current Research International (2020) Vol. 20, Issue 4, Article no.ACRI.57840, 22-47. doi:10.9734/ACRI/2020/v20i430187 (A000073, A000931, A001608, A001609, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A128587, A159284, A176971, A226308, A276225, A276228)
Yüksel Soykan, A Study on Generalized Fibonacci Numbers: Sum Formulas Sum_{k=0..n} kx^k W_k³ and Sum_{k=1..n} kx^k W_−k³ for the Cubes of Terms, Earthline Journal of Mathematical Sciences (2020) Vol. 4, No. 2, 297-331. doi:10.34198/ejms.4220.297331 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, Generalized Pell-Padovan Numbers, Asian Journal of Advanced Research and Reports (2020) Vol. 11, No. 2, 8-28, Article No. 57839. doi:10.9734/AJARR/2020/v11i230259 (A008346, A066983, A099925)
Yüksel Soykan, On Sum Formulas for Generalized Tribonacci Sequence, Journal of Scientific Research and Reports (2020) Vol. 26, Issue 7. doi:10.9734/jsrr/2020/v26i730283
Yüksel Soykan, Properties of Generalized 6-primes Numbers, Archives of Current Research International (2020) Vol. 20, No. 6, 12-30, Article No. ACRI.60386. doi:10.9734/ACRI/2020/v20i630199
Yüksel Soykan, Properties of Generalized (r, s, t, u)-Numbers, Earthline J. of Math. Sci. (2021) Vol. 5, No. 2, 297-327. doi:10.34198/ejms.5221.297327 (A000078, A007907, A073817, A103142, A190139, A226309, A331413)
Yüksel Soykan, On Generalized (r, s)-numbers, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 8, No. 1, 1–14. (A000045, A000032, A000129, A001045, A002203, A014551)
Yüksel Soykan, On Generalized Tetranacci Numbers: Closed Form Formulas of the Sum Σⁿ_k=0 W_k² of the Squares of Terms, Int. J. Adv. Appl. Math. and Mech. (2020) Vol. 8, No. 1, 15-26. (A000078, A073817, A103142, A190139, A331413)
Yüksel Soykan, A study on sum formulas of generalized sixth-order linear recurrence sequences, Asian J. of Advanced Research and Reports (2020) Vol. 14, Issue 2, 36-48. doi:10.9734/ajarr/2020/v14i230329
Yüksel Soykan, Corrigendum: On summing formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers, Advances in Research (2020) Vol. 21, No. 10, Article no. AIR.51824, 66-82. doi:10.9734/AIR/2020/v21i1030253 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, A Study on Sum Formulas of Generalized Tetranacci Numbers: Closed Forms of the Sum Formulas Σⁿ_k=0 kW_k and Σⁿ_k=1 kW_−k, Zonguldak Bülent Ecevit University (Turkey, 2021). PDF (A000078, A007909, A073817, A103142, A190139, A226309, A331413)
Yüksel Soykan, On the Sums of Squares of Generalized Tribonacci Numbers: Closed Formulas of Sum_{k=0..n} x^k × W_k², Advanced Open Peer Review (2021). PDF (A000073, A000931, A001608, A001609, A001644, A057597, A066983, A072328, A073145, A077939, A077947, A077978, A077997, A078012, A078049, A078712, A128587, A159284, A176971, A226308, A276225, A276228)
Yüksel Soykan, Notes on Binomial Transform of the Generalized Narayana Sequence, Earthline J. Math. Sci. (2021) Vol. 7, No. 1, 77-111. doi:10.34198/ejms.7121.77111 (A000930, A001609, A078012)
Yüksel Soykan, Some Properties of Generalized Fibonacci Numbers: Identities, Recurrence Properties and Closed Forms of the Sum Formulas Σⁿ_k=0 x^k W_(mk+j), Archives of Current Res. Int'l (2021) Vol. 21, No. 3, 11-38. doi:10.9734/ACRI/2021/v21i330235 (A000032, A000045, A000129, A001045, A002203, A014551)
Yüksel Soykan, Sums and Partial Sums of Horadam Sequences: The Sum Formulas Σ_k=0ⁿ x^kW_k and Σ_k=0^n+m x^kW_k via Generating Functions, Int. J. Adv. Appl. Math. and Mech. (2022), Vol. 9, No. 3, 33-40. PDF (A000032, A000045, A000051, A000129, A000225, A001045, A001109, A002203, A003499, A001541, A014551, A15518, A046717, A102345)
Yüksel Soykan, Sum Formulas of Generalized Pentanacci Numbers: Closed Forms of the Sum Formulas Sum_{k=0…n} k × W_k and Sum_{k=1…n} k × W_−k, Int. J. Adv. Appl. Math. and Mech. (2021), Vol. 8, No. 4, 1–14. PDF (A001591, A074048, A141448, A226310, A226311)
Yüksel Soykan, Generalized Edouard Numbers, Int. J. Adv. Appl. Math. and Mech. (2022), Vol. 9, No. 3, 41-52. PDF (A53142, A081555)
Yüksel Soykan, Generalized John Numbers, J. Progressive Res. Math. (2022) Vol 19, No. 1. Abstract (A000129, A002203)
Yüksel Soykan and Melih Göcen, Properties of hyperbolic generalized Pell numbers, Notes on Number Theory and Disc. Math. (2020) Vol. 26, No. 4, 136-153. doi:10.7546/nntdm.2020.26.4.136-153 (A000129, A002203)
Yüksel Soykan, Mehmet Gümüş, Melih Göcen, A Study On Dual Hyperbolic Generalized Pell Numbers, Zonguldak Bülent Ecevit University (Zonguldak, Turkey, 2019). doi:10.13140/RG.2.2.21008.97289 (A000129, A002203)
Yüksel Soykan, İnci Okumuş, On a Generalized Tribonacci Sequence, Journal of Progressive Research in Mathematics (JPRM, 2019) Vol. 14, Issue 3, 2413-2418. Abstract (A000073, A001644)
Yüksel Soykan, İnci Okumuş, and Nazmiye Gönül Bilgin, On Generalized Bigollo Numbers, Asian Res. J. Math. (2023) Vol. 19, No. 8, 72-88, Art. No. 99811. doi:10.9734/ARJOM/2023/v19i8689 (A000051, A000215, A000225, A000295, A052548)
Yüksel Soykan, İnci Okumuş, Melih Göcen, On Generalized Tetranacci Quaternions, Bülent Ecevit Üniversitesi (Turkey, 2019), Preprints (2019), 2019030129. doi:10.20944/preprints201903.0129.v1
Yüksel Soykan and Evren Eyican Polatlı, Properties of Generalized Sixth Order Jacobsthal Sequence, Int. J. Adv. Appl. Math. and Mech. (2021) Vol. 8, No. 3, 24–40. PDF (A001045)
Yüksel Soykan, Erkan Taşdemir, and Can Murat Dikmen, On the sum of the cubes of generalized balancing numbers: The sum formula ∑_k=0ⁿ x^kW_mk+j³, Open J. Math. Sci. (2022) Vol. 6, 152-167. doi:10.30538/oms2022.0184 (A001109, A001541)
Yüksel Soykan, Erkan Taşdemir, İnci Okumuş, On Dual Hyperbolic Numbers With Generalized Jacobsthal Numbers Components, Zonguldak Bülent Ecevit University, (Zonguldak, Turkey, 2019). doi:10.13140/RG.2.2.13499.36641 (A001045, A014551)
Yüksel Soykan, Erkan Taşdemir, İnci Okumuş, Melih Göcen, Gaussian Generalized Tribonacci Numbers, Journal of Progressive Research in Mathematics (JPRM, 2018) Vol. 14, Issue 2, 2373-2387. PDF (A000073, A001644)
Yüksel Soykan, A Study on Generalized Tetranacci Numbers: Closed Form Formulas Σ _k=0ⁿ x^kW_k² of Sums of the Squares of Terms, Asian Research J. of Math. (2020) Vol. 16, No. 10, Article no.ARJOM.62560, 109-136. doi:10.9734/ARJOM/2020/v16i1030234 (A000078, A007909, A073817, A103142, A190139, A226309, A331413)
Yüksel Soykan, Recurrence Properties of Generalized Hexanacci Sequence, Asian J. of Adv. Res. And Reports (2021) Vol. 15, No. 2, 85-93, Article no. AJARR.66969. doi:10.9734/AJARR/2021/v15i230370 (A001592, A074584)
Quico Spaen, Christopher Thraves Caro, Mark Velednitsky, The Dimension of Valid Distance Drawings of Signed Graphs, Discrete & Computational Geometry (2019), 1-11. doi:10.1007/s00454-019-00114-w (A000088)
George Spahn and Doron Zeilberger, Counting Permutations Where The Difference Between Entries Located r Places Apart Can never be s (For any given positive integers r and s), arXiv:2211.02550 [math.CO], 2022. (A000255, A002464, A055790, A110128, A117574, A189255, A189281, A189282, A189283, A189284, A277563, A277609, A280425)
Amelia Carolina Sparavigna, On Repunits, Politecnico di Torino (2019). doi:10.5281/zenodo.2639620 (A002275)
Amelia Carolina Sparavigna, On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers, Politecnico di Torino (2019). doi:10.5281/zenodo.2634312 (A000051, A000225, A002064, A003261)
Amelia Carolina Sparavigna, A recursive formula for Thabit numbers, Politecnico di Torino (2019). doi:10.5281/zenodo.2638790 (A007505)
Amelia Carolina Sparavigna, Composition Operations of Generalized Entropies Applied to the Study of Numbers, International Journal of Sciences (2019) Vol. 8, No. 4, 87-92. doi:10.18483/ijSci.2044 (A000051, A000225, A002064, A002275, A003261, A007505)
Amelia Carolina Sparavigna, Groupoids of OEIS A002378 and A016754 Numbers (oblong and odd square numbers), Politecnico di Torino (Italy, 2019). Abstract (A002378, A016754)
Amelia Carolina Sparavigna, Groupoid of OEIS A001844 Numbers (centered square numbers), Politecnico di Torino, Italy. doi:10.5281/zenodo.3252339 (A001844)
Amelia Carolina Sparavigna, Discussion of the groupoid of Proth numbers (OEIS A080075), Politecnico di Torino, Italy. doi:10.5281/zenodo.3339313 (A080075, A116882, A157892, A157893)
Amelia Carolina Sparavigna, Groupoid of OEIS A003154 Numbers (star numbers or centered dodecagonal numbers), Department of Applied Science and Technology, Politecnico di Torino (Italy, 2019). doi:10.5281/zenodo.3387054 (A003154)
Amelia Carolina Sparavigna, Binary Operators of the Groupoids of OEIS A093112 and A093069 Numbers (Carol and Kynea Numbers), Department of Applied Science and Technology, Politecnico di Torino (Italy, 2019). doi:10.5281/zenodo.3240465 (A093069, A093112)
Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT]. doi:10.5281/zenodo.3471358 Abstract (A000051, A000217, A000225, A000384, A001348, A002064, A002275, A002283, A002378, A002943, A003261, A014105, A014635, A022266, A024023, A024049, A024062, A024075, A033585, A034474, A045945, A046092, A050915, A051682, A052539, A060352, A060416, A062725, A062741, A064748, A064756, A081266, A093069, A093112, A139274, A139276, A178572) As we can easily see, other integer sequences can have the same binary operators, and therefore can be used to represent the related groupoids. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we can also identify the properties of these representations of groupoids. At the same time, we can also find integer sequences not given in OEIS and probably not yet studied. Using the On-Line Encyclopedia of Integer Sequences (OEIS), we have seen that quite different sequences can have the same binary operators. We have also found integer sequences not given in OEIS and that need to be studied.
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019). doi:10.5281/zenodo.3470205 (A000217, A000384, A014105, A014635, A022266, A033585, A062725, A062741, A081266, A139274, A139276, A178572, A331190)
Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10. doi:10.18483/ijSci.2188 (A000051, A000225, A001348, A002064, A002275, A002283, A003261, A024023, A024049, A024062, A034472, A034474, A046092, A050914, A050915, A052539, A060352, A062394, A060416, A064756, A093069, A093112)
Amelia Carolina Sparavigna, Binary operations applied to numbers, Politecnico di Torino (Italy 2020). PDF (A000217, A001844, A002378, A002275, A003154, A016754, A080075, A093069, A093112)
Amelia Carolina Sparavigna, The Pentagonal Numbers and their Link to an Integer Sequence which contains the Primes of Form 6n−1, Politecnico di Torino (Italy, 2021). doi:10.5281/zenodo.4641886 (A000326, A005449, A007528, A016969)
Amelia Carolina Sparavigna, Generalized sums of Fibonacci and Lucas Numbers, Politecnico di Torino (Italy, 2021). doi:10.5281/zenodo.4656051 (A000032, A000045)
Amelia Carolina Sparavigna, Binary operations inspired by generalized entropies applied to figurate numbers, Politecnico di Torino (Italy, 2021). doi:10.5281/zenodo.4662489 (A000326, A007528, A016838, A016969)
Amelia Carolina Sparavigna, Generalized Sum of Stella Octangula Numbers, Politecnico di Torino (Italy, 2021). doi:10.5281/zenodo.4662348 (A002378, A003154, A007588, A033431)
Amelia Carolina Sparavigna, Cardano Formula and Some Figurate Numbers, Politecnico di Torino (Italy, 2021). doi:10.5281/zenodo.4663050 (A007588, A033431)
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Michael Z. Spivey, Staircase rook polynomials and Cayley's game of Mousetrap, European Journal of Combinatorics, Volume 30, Issue 2, February 2009, Pages 532-539.
Michael Z. Spivey and Laura L. Steil, "The k-Binomial Transforms and the Hankel Transform", J. Integer Sequences, Volume 9, 2006, Article 06.1.1.
Robin James Spivey, Close encounters of the golden and silver ratios, Notes on Number Theory and Discrete Mathematics (2019) Vol. 25, No. 3, 170–184. doi:10.7546/nntdm.2019.25.3.170-184 (A000032, A000045, A000129, A002203, A013946)
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R. P. Stanley, Hipparchus, Plutarch, Schroeder and Hough, American Mathematical Monthly 104 (1997), 344-350.
Richard P. Stanley, "The Descent Set and Connectivity Set of a Permutation", J. Integer Sequences, Volume 8, 2005, Article 05.3.8.
R. P. Stanley, An Equivalence Relation on the Symmetric Group and Multiplicity-free Flag h-Vectors, PDF
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Richard P. Stanley, Theorems and Conjectures on Some Rational Generating Functions, arXiv:2101.02131 [math.CO], 2021. (A014675, A104767)
Richard P. Stanley, Some enumerative applications of cyclotomic polynomials, MIT, 2024. See p. 15. PDF (A120963)
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R. P. Stanley, F. Zanello, Some asymptotic results on q-binomial coefficients, PDF, 2014 and Ann. Combinat. 20 (2016) 623-634 doi:10.1007/s00026-016-0319-8
Richard P. Stanley, Fabrizio Zanello, The Catalan case of Armstrong's conjecture on simultaneous core, SIAM Journal on Discrete Mathematics (2015) 29(1), 658-666. doi:10.1137/130950318 Also arXiv:1312.4352 (A005585, A006419)
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Daniel W. Stasiuk, An Enumeration Problem for Sequences of n-ary Trees Arising from Algebraic Operads, Master’s Thesis, University of Saskatchewan-Saskatoon (2018). PDF (A002054, A002694, A002696, A003516, A004321, A004334, A013698)
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Jeremy G. Sumner, Michael D. Woodhams, Lie-Markov models derived from finite semigroups, arXiv:1709.00520 [math.GR], 2017.
Brian Y. Sun, Baoyindureng Wu, Two-log-convexity of the Catalan-Larcombe-French sequence, Journal of Inequalities and Applications, 2015, 2015:404; doi:10.1186/s13660-015-0920-0.
Brian Y. Sun, JX Meng, Proof of a Conjecture of Z.-W. Sun on Trigonometric Series, arXiv preprint arXiv:1606.08153, 2016.
Nathan Sun, On d-permutations and Pattern Avoidance Classes, arXiv:2208.08506 [math.CO], 2022. (A000290, A001787, A003946, A006130, A016777, A026150, A047732)
Ping Sun, Enumeration of standard Young tableaux of shifted strips with constant width, arXiv preprint arXiv:1506.07256, 2015 Also Electronic Journal of Combinatorics, Volume 24(2), 2017, #P2.41.
Ping Sun, Enumeration formulas for standard Young tableaux of nearly hollow rectangular shapes, Discrete Mathematics, 341 (2018), 1144-1149. doi:10.1016/j.disc.2017.10.005
Ping Sun, On the moments of normal distributions and numbers of standard Young tableaux, Adv. in Appl. Math. (2021) Vol. 130, 102230. doi:10.1016/j.aam.2021.102230
Qifu Tyler Sun, Hanqi Tang, Zongpeng Li, Xiaolong Yang, Keping Long, Circular-shift Linear Network Codes with Arbitrary Odd Block Lengths, arXiv:1806.04635 [cs.IT], 2018. (A001122)
Xinyu Sun, "New Lower Bound On The Number of Ternary Square-Free Words", J. Integer Sequences, Volume 6, 2003, Article 03.3.2.
Yidong Sun, The Star of David Rule (2008); arXiv:0805.1277; Linear Algebra and its Applications, Volume 429, Issues 8-9, 16 October 2008, Pages 1954-1961.
Yidong Sun and Fei Ma, Four transformations on the Catalan triangle, arXiv preprint arXiv:1305.2017, 2013
Yidong Sun and Fei Ma, Minors of a Class of Riordan Arrays Related to Weighted Partial Motzkin Paths, arXiv preprint arXiv:1305.2015, 2013
Yidong Sun and Fei Ma, Some new binomial sums related to the Catalan triangle, Electronic Journal of Combinatorics 21(1) (2014), #P1.33
Sun, Yidong; Ma, Luping doi:10.1016/j.ejc.2014.01.004 Minors of a class of Riordan arrays related to weighted partial Motzkin paths. Eur. J. Comb. 39, 157-169 (2014).
Yidong Sun and Zhiping Wang, Pattern Avoidance in Generalized Non-crossing Trees (2008); arXiv:0805.1280
Yidong Sun and Zhiping Wang, String pattern avoidance in generalized non-crossing trees, Disc. Math. Theor. Comp. Sci. 11 (2009) 79-94.
Sun, Yidong; Wu, Xiaojuan The largest singletons of set partitions. European J. Combin. 32 (2011), no. 3, 369-382.
Sun, Yidong; Xu, Yanjie The largest singletons in weighted set partitions and its applications. Discrete Math. Theor. Comput. Sci. 13 (2011), no. 3, 75-85.
Yidong Sun, Liting Zhai, Some properties of a class of refined Eulerian polynomials, arXiv:1810.07956 [math.CO], 2018. (A000111, A008292)
Zhe Sun, T Suenaga, P Sarkar, S Sato, M Kotani, H Isobe, Stereoisomerism, crystal structures, and dynamics of belt-shaped cyclonaphthylenes, Proc. Nath. Acead. Sci. USA, vol. 113 no. 29, pp. 8109–8114, doi:10.1073/pnas.1606530113
Zhi-Hong Sun, "Expansion and identities concerning Lucas Sequences", The Fibonacci Quarterly, Volume 44, May 2006, pages 145-153.
Sun, Zhi-Hong Congruences concerning Lucas sequences. Int. J. Number Theory 10 (2014), no. 3, 793-815.
Zhi-Hong Sun, Congruences for Domb and Almkvist-Zudilin numbers, Integral Transforms & Special Functions, Vol. 26 Issue 8, p642-659, 2015, doi:10.1080/10652469.2015.1034122
Zhi-Hong Sun, Supercongruences involving Euler polynomials, Proc. American Mathematical Society, 144 (2016), 3295-3308.
Zhi-Hong Sun, Congruences for Apéry-like numbers, arXiv:1803.10051 [math.NT], 2018. (A000172, A002825, A002893, A005258, A005259, A053175, A093388, A125143, A290575, A291898).
Zhi-Hong Sun, Super congruences concerning binomial coefficients and Apéry-like numbers, arXiv:2002.12072 [math.NT], 2020. (A002895, A125143, A291898)
Zhi-Wei Sun, doi:10.1016/j.jnt.2011.06.005 On Delannoy numbers and Schroeder numbers, J. Number Theory 131 (2011) 2387-2397; arXiv:1009.2486.
Zhi-Wei Sun, On sums involving products of three binomial coefficients, arXiv:1012.3141 and Acta Arith. 156 (2) (2012) 123-141 doi:10.4064/aa156-2-2
Sun, Zhi-Wei, p-adic valuations of some sums of multinomial coefficients. Acta Arith. 148 (2011), no. 1, 63-76.
Z.-W. Sun, Conjectures involving arithmetical sequences, Number Theory: Arithmetic in Shangrila (eds., S. Kanemitsu, H.-Z. Li and J.-Y. Liu), Proc. the 6th China-Japan Sem. Number Theory (Shanghai, August 15-17, 2011), World Sci., Singapore, 2013, pp. 244-258; PDF.
Zhi-Wei Sun, Conjectures involving combinatorial sequences, Arxiv preprint arXiv:1208.2683, 2012
Zhi-Wei Sun, On sums of Apery polynomials and related congruences. J. Number Theory 132 (2012) 2673-2699 doi:10.1016/j.jnt.2012.05.014
Z.-W. Sun, Conjectures involving primes and quadratic forms, arXiv preprint arXiv:1211.1588, 2012
Zhi-Wei Sun, Products and Sums Divisible by Central Binomial Coefficients, Electronic Journal of Combinatorics, 20(1) (2013), #P9.
Z.-W. Sun, Fibonacci numbers modulo cubes of primes, arXiv:0911.3060; Taiwanese J. Math. 17 (2013). doi:10.11650/tjm.17.2013.2488
Z.-W. Sun, Connections between p = x^2+ 3y^2 and Franel numbers, J. Number Theory 133 (2013), no. 9, 2914-2928.
Z.-W. Sun On some determinants with Legendre symbol entries, 2013; PDF
Z.-W. Sun, Some new problems in additive combinatorics, arXiv preprint arXiv:1309.1679, 2013
Z.-W. Sun, On a^n+ bn modulo m, arXiv preprint arXiv:1312.1166, 2013
ZW SUN, A conjecture on unit fractions involving primes, Preprint 2015; http://maths.nju.edu.cn/~zwsun/UnitFraction.pdf
Sun, Zhi-Wei On functions taking only prime values. J. Number Theory 133 (2013), no. 8, 2794-2812.
Sun, Zhi-Wei Congruences for Franel numbers. Adv. in Appl. Math. 51 (2013), no. 4, 524-535.
Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014-2016. (A236832)
Z.-W. Sun, New observations on primitive roots modulo primes, arXiv preprint arXiv:1405.0290, 2014
Z.-W. Sun, Congruences involving g_n(x) = Sum_{k= 0..n} C(n,k)^2 C(2k,k) x^k, arXiv preprint arXiv:1407.0967, 2014
Sun, Zhi-Wei Congruences involving generalized central trinomial coefficients. Sci. China Math. 57 (2014), no. 7, 1375-1400.
Z.-W. Sun, A result similar to Lagrange's theorem, arXiv preprint arXiv:1503.03743, 2015
Zhi-Wei Sun, Refining Lagrange's four-square theorem, arXiv:1604.06723, 2016.
Zhi-Wei Sun, Conjectures on representations involving primes, In: M. Nathanson (ed.), Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer Proc. in Math. & Stat., Vol. 220, Springer, New York, 2017, pp. 279-310; http://maths.nju.edu.cn/~zwsun/176r.pdf
Zhi-Wei Sun, Some new series for 1/π motivated by congruences, arXiv:2009.04379 [math.NT], 2020. (A337247, A337332 in references)
Zhi-Wei Sun, New Conjectures of Representations of Integers (I), Nanjing Univ. J. Math. Biquarterly 34 (2017), No. 2, 97-120. [PDF]. (A260418, A262827, A266152, A266153, A266212, A266215, A266230, A266231, A266277, A266314, A266363, A266364, A266528, A266548, A266985, A267861, A271076, A271099, A271169, A271237, A275150, A280153, A280356, A290491)
Zhi-Wei Sun, Quadratic residues and related permutations and identities, arXiv:1809.07766 [math.NT], 2018. (A319311, A319882, A319894, A319903, A320044)
Zhi-Wei Sun, On permutations of {1, ..., n} and related topics, arXiv:1811.10503 [math.CO], 2018. (A073112, A073364, A126972, A321597, A321610, A321611, A321727, A322069, A322070, A322099, A322363)
Zhi-Wei Sun, On some determinants with Legendre symbol entries, Finite Fields and Their Applications (2019) Vol. 56, 285-307. doi:10.1016/j.ffa.2018.12.004
Zhi-Wei Sun, On some determinants involving the tangent function, arXiv:1901.04837 [math.NT], 2019. (A277445)
Zhi-Wei Sun, Riddles of Representations of Integers, presentation to Nanjing Normal Univ. (China, 2019). PDF (A286944)
Zhi-Wei Sun, Sums of four squares with certain restrictions, arXiv:2010.05775 [math.NT], 2020. (A335624, A337082, A338019, A338094, A338095, A338096, A338103, A338119, A338121, A338139)
Zhi-Wei Sun, Various Refinements of Lagrange's Four-Square Theorem, Westlake Number Theory Symposium (Nanjing University, China, 2020). PDF (A308734)
Zhi-Wei Sun, On permutations of {1, …, n} and related topics, J. of Algebraic Combinatorics (2021). doi:10.1007/s10801-021-01028-8 (A126972)
Zhi-Wei Sun, On some determinants involving the tangent function, arXiv:1901.04837 [math.NT], 2019. See pp. 18, 20. (A277445)
Zhi-Wei Sun and Roberto Tauraso, Congruences involving Catalan numbers (2007), arXiv:0709.1665.
Z-W. Sun and R. Tauraso, doi:10.1016/j.aam.2010.01.001 New congruences for central binomial coefficients, Adv. Appl Math 45 (1) (2010) 125-148
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