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

1, 6, 66, 901, 13881, 231008, 4057660, 74174927, 1398295989, 27012396022, 532327974882, 10665521789203, 216696065279573, 4455636282185802, 92567760074841818

Offset: 1

Author

N. J. A. Sloane, Jul 12 2009

Keywords

• nonn
• more

References

• Anthony J. Guttmann, editor. Polygons, Polyominoes and Polycubes, volume 775 of Lecture Notes in Physics. Springer-Verlag, Heidelberg, 2009.

Links

• J. Adler, Y. Meir, A. B. Harris, A. Aharony, and J. A. M. S. Duarté, Series study of random animals in general dimensions, Physical Review B, 38 (1988) 4941.
• Gadi Aleksandrowicz and Gill Barequet, Counting polycubes without the dimensionality curse, Discrete Mathematics, 309 (2009), 4576-4583.
• Gadi Aleksandrowicz and Gill Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.
• Gadi Aleksandrowicz and Gill 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, 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).
• 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.
• Ronnie Barequet, Gill Barequet, and Günter Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica 30, 257-275 (2010).
• 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.
• 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 trees, Journal of Statistical Physics, 102(3/4) (2001) 865-881.
• Sebastian Luther and Stephan Mertens, Counting lattice animals in high dimensions, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565. See Table 2 for the terms (but beware of the incorrect a(13)!) or Table 3 for the formulas.
• Sebastian Luther and Stephan 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.

Crossrefs

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

Programs

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 *)

Formula

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

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

a(13) corrected by M. F. Hasler, Jun 26 2025