

A151832


Number of fixed 6dimensional polycubes with n cells.


7



1, 6, 66, 901, 13881, 231008, 4057660, 74174927, 1398295989, 27012396022, 532327974882, 10665521789203, 227093585071305, 4455636282185802, 92567760074841818
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OFFSET

1,2


REFERENCES

G. Aleksandrowicz and G. Barequet, Counting ddimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215229.
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, SpringerVerlag, 9099, 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 highdimensional polycubes, Combinatorica, 30 (2010), 257275.
Anthony J. Guttmann, editor. Polygons, Polyominoes and Polycubes, volume 775 of Lecture Notes in Physics. SpringerVerlag, Heidelberg, 2009. [Jonathan Vos Post, Oct 10 2011]
D.S. Gaunt and P.J. Peard. 1/dexpansions for the free energy of weakly embedded site animal models of branched polymers. Journal of Physics A: Mathematical and General, 33 (2000) 75157539. [Jonathan Vos Post, Oct 10 2011]
S. Luther and S. Mertens, Counting lattice animals in high dimensions,
Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546565.


LINKS

Table of n, a(n) for n=1..15.
J. Adler, Y. Meir, A.B. Harris, A. Aharony, and J.A.M.S. Duarte. Series study of random animals in general dimensions Physical Review B, 38 (1988) 4941.
G. Aleksandrowicz and G. Barequet, Counting polycubes without the dimensionality curse, Discrete Mathematics, 309 (2009), 45764583.
Gill Barequet, Gil BenShachar, Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 1618 March 2020).
HsiaoPing Hsu, Walter Nadler, and Peter Grassberger. Statistics of lattice animals. Computer Physics Communications, 169 (2005) 114116.
Iwan Jensen. Enumerations of lattice animals and treesJournal of Statistical Physics, 102(3/4) (2001) 865881.
S. Luther and S. Mertens, Counting lattice animals in high dimensions, arXiv:1106.1078
Stephan Mertens and Markus E. Lautenbacher. Counting lattice animals: A parallel attack J. Stat. Phys. 66 (1992) 669


FORMULA

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


MATHEMATICA

A048667 = Cases[Import["https://oeis.org/A048667/b048667.txt", "Table"], {_, _}][[All, 2]];
a[n_] := A048667[[n]]/n;
Array[a, 15] (* JeanFrançois Alcover, Sep 12 2019 *)


CROSSREFS

Cf. A001931, A048667, A151830, A151831, A151833, A151834, A151835.
Sequence in context: A124862 A130977 A191096 * A133306 A216636 A169715
Adjacent sequences: A151829 A151830 A151831 * A151833 A151834 A151835


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jul 12 2009


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


STATUS

approved



