A151834 Number of fixed 8-dimensional polycubes with n cells.

1, 8, 120, 2276, 49204, 1156688, 28831384, 750455268, 20196669078, 558157620384, 15762232227968, 453181069339660, 13228272325440164, 391166062869849024

Offset

1,2

Comments

a(1)-a(10) can be computed by formulas in Barequet et al. (2010). Luther and Mertens confirm these values (and add two more) by direct counting.

Links

Table of n, a(n) for n=1..14.

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, 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).

Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes; in: Handbook of Discrete and Computational Geometry, Chapman and Hall/CRC, 2017. (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.

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), P09026.

Stephan Mertens, Lattice Animals

Crossrefs

Cf. A001931, A151830, A151831, A151832, A151833, A151835.

Sequence in context: A239226 A133308 A191098 * A007762 A211825 A113383

Adjacent sequences: A151831 A151832 A151833 * A151835 A151836 A151837

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

a(13)-a(14) from Mertens added by Andrey Zabolotskiy, Jan 29 2023

Status

approved