

A171860


Number of ncell fixed polycubes that are proper in n2 dimensions.


6



0, 1, 17, 348, 8640, 254800, 8749056, 343901376, 15257600000, 755110160640, 41278242816000, 2471677136321536, 160961785787056128, 11330322120000000000, 857485369051342438400, 69444841895469240729600, 5993559601317659925282816, 549242871950650346384195584
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OFFSET

2,3


REFERENCES

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
G. Barequet, M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, 31st International Symposium on Computational Geometry (SoCG'15). Editors: Lars Arge and János Pach; pp. 1922, 2015.
R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of highdimensional polycubes, Combinatorica, 30 (2010), 257275. See Th. 6.


LINKS



FORMULA

a(n) = 2^(n3)*n^(n5)*(n2)*(2*n^2  6*n + 9).


PROG

(Magma) [2^(n3)*n^(n5)*(n2)*(2*n^26*n+9): n in [2..20]]; // Vincenzo Librandi, May 26 2011


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



