A151832 Number of fixed 6-dimensional polycubes with n cells.

1, 6, 66, 901, 13881, 231008, 4057660, 74174927, 1398295989, 27012396022, 532327974882, 10665521789203, 227093585071305, 4455636282185802, 92567760074841818

Offset

1,2

References

G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.

G. Aleksandrowicz and G. Barequet, Parallel enumeration of lattice animals, Proc. 5th Int. Frontiers of Algorithmics Workshop, Zhejiang, China, Lecture Notes in Computer Science, 6681, Springer-Verlag, 90-99, May 2011.

Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) Preprint, 2016, http://www.csun.edu/~ctoth/Handbook/chap14.pdf

R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica, 30 (2010), 257-275.

Anthony J. Guttmann, editor. Polygons, Polyominoes and Polycubes, volume 775 of Lecture Notes in Physics. Springer-Verlag, Heidelberg, 2009. [Jonathan Vos Post, Oct 10 2011]

D.S. Gaunt and P.J. Peard. 1/d-expansions for the free energy of weakly embedded site animal models of branched polymers. Journal of Physics A: Mathematical and General, 33 (2000) 7515-7539. [Jonathan Vos Post, Oct 10 2011]

S. Luther and S. Mertens, Counting lattice animals in high dimensions,

Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565.

Links

Table of n, a(n) for n=1..15.

J. Adler, Y. Meir, A.B. Harris, A. Aharony, and J.A.M.S. Duarte. Series study of random animals in general dimensions Physical Review B, 38 (1988) 4941.

G. Aleksandrowicz and G. Barequet, Counting polycubes without the dimensionality curse, Discrete Mathematics, 309 (2009), 4576-4583.

Gill Barequet, Gil Ben-Shachar, and Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020).

Hsiao-Ping Hsu, Walter Nadler, and Peter Grassberger. Statistics of lattice animals. Computer Physics Communications, 169 (2005) 114-116.

Iwan Jensen, Enumerations of lattice animals and treesJournal of Statistical Physics, 102(3/4) (2001) 865-881.

S. Luther and S. Mertens, Counting lattice animals in high dimensions, arXiv:1106.1078 [cond-mat.stat-mech], 2011.

Stephan Mertens and Markus E. Lautenbacher. Counting lattice animals: A parallel attack J. Stat. Phys. 66 (1992) 669

Formula

a(n) = A048667(n)/n. - Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A048667.

Mathematica

A048667 = Cases[Import["https://oeis.org/A048667/b048667.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A048667[[n]]/n;
Array[a, 15] (* Jean-François Alcover, Sep 12 2019 *)

Crossrefs

Cf. A001931, A048667, A151830, A151831, A151833, A151834, A151835.

Sequence in context: A124862 A130977 A191096 * A133306 A371681 A216636

Adjacent sequences: A151829 A151830 A151831 * A151833 A151834 A151835

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 12 2009

Extensions

a(10) from Gadi Aleksandrowicz (gadial(AT)gmail.com), Mar 21 2010

a(11)-a(15) from Luther and Mertens by Gill Barequet, Jun 12 2011

Status

approved