A051869 17-gonal (or heptadecagonal) numbers: a(n) = n*(15*n-13)/2.

0, 1, 17, 48, 94, 155, 231, 322, 428, 549, 685, 836, 1002, 1183, 1379, 1590, 1816, 2057, 2313, 2584, 2870, 3171, 3487, 3818, 4164, 4525, 4901, 5292, 5698, 6119, 6555, 7006, 7472, 7953, 8449, 8960, 9486, 10027, 10583, 11154, 11740, 12341

Offset

0,3

Comments

Sequence found by reading the line from 0, in the direction 0, 17,... and the parallel line from 1, in the direction 1, 48,..., in the square spiral whose vertices are the generalized 17-gonal numbers. - Omar E. Pol, Jul 18 2012

References

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index to sequences related to polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(1+14*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = a(n-1) + 15*n - 14 with n>0, a(0)=0. - Vincenzo Librandi, Aug 06 2010

a(n) = A226489(n) - n. - Bruno Berselli, Jun 11 2013

a(15*a(n) + 106*n + 1) = a(15*a(n) + 106*n) + a(15*n+1). - Vladimir Shevelev, Jan 24 2014

E.g.f.: x*(2 + 15*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019

Product_{n>=2} (1 - 1/a(n)) = 15/17. - Amiram Eldar, Jan 22 2021

Maple

A051869 := proc(n) n*(15*n-13)/2 ; end proc: seq(A051869(n), n=0..30) ; # R. J. Mathar, Feb 05 2011

Mathematica

Table[n*(15*n - 13)/2, {n, 0, 40}] (* Robert Price, Oct 11 2018 *)
PolygonalNumber[17, Range[0, 50]] (* Harvey P. Dale, Dec 14 2022 *)

Prog

(PARI) a(n)=n*(15*n-13)/2 \\ Charles R Greathouse IV, Jan 24 2014
(Magma) [n*(15*n-13)/2: n in [0..40]]; // G. C. Greubel, Aug 30 2019
(Sage) [n*(15*n-13)/2 for n in (0..40)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n-> n*(15*n-13)/2); # G. C. Greubel, Aug 30 2019

Crossrefs

Cf. A002378.

Sequence in context: A362480 A159850 A031122 * A297818 A297988 A210372

Adjacent sequences: A051866 A051867 A051868 * A051870 A051871 A051872

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 1999

Status

approved