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

Author

N. J. A. Sloane, Jul 12 2009

Keywords

• nonn
• more

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

• 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).

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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