A151831 Number of fixed 5-dimensional polycubes with n cells.

1, 5, 45, 495, 6095, 80617, 1121075, 16177405, 240196280, 3648115531, 56440473990, 886696345225, 14111836458890, 227093585071305, 3689707621144614

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.

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.

G. Aleksandrowicz and G. Barequet, counting d-dimensional polycubes and nonrectangular planar polyomnoes, Lect. Not. Comp. Sci 4112 (2006) 418-427 Table 2

Gill Barequet, Gil Ben-Shachar, 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).

Formula

a(n) = A048666(n)/n. - Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A048666.

Mathematica

A048666 = Cases[Import["https://oeis.org/A048666/b048666.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A048666[[n]]/n;
Array[a, 15] (* Jean-François Alcover, Sep 12 2019 *)

Crossrefs

Cf. A001931, A048666, A151830, A151832, A151833, A151834, A151835.

Sequence in context: A202825 A195188 A232730 * A233834 A188267 A133305

Adjacent sequences: A151828 A151829 A151830 * A151832 A151833 A151834

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 12 2009

Extensions

a(14) and a(15) from Luther and Mertens by Gill Barequet, Jun 12 2011

Status

approved