A151833 Number of fixed 7-dimensional polycubes with n cells.

1, 7, 91, 1484, 27468, 551313, 11710328, 259379101, 5933702467, 139272913892, 3338026689018, 81406063278113, 2014611366114053, 50486299825273271

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

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..14.

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) = A048668(n)/n. - Jean-François Alcover, Sep 12 2019, after Andrew Howroyd in A048668.

Mathematica

A048668 = Cases[Import["https://oeis.org/A048668/b048668.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A048668[[n]]/n;
Array[a, 14] (* Jean-François Alcover, Sep 12 2019 *)

Crossrefs

Cf. A001931, A048668, A151830, A151831, A151832, A151834, A151835.

Sequence in context: A191097 A234570 A133307 * A113372 A131940 A008542

Adjacent sequences: A151830 A151831 A151832 * A151834 A151835 A151836

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 12 2009

Extensions

More terms from Gadi Aleksandrowicz (gadial(AT)gmail.com), Mar 21 2010

a(11)-a(14) from Luther and Mertens by Gill Barequet, Jun 12 2011

Status

approved