

A171860


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


3



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

Vincenzo Librandi, Table of n, a(n) for n = 2..100
A. Asinowski, G. Barequet, R. Barequet, G. Rote, Proper nCell Polycubes in n3 Dimensions, J. Int. Seq. 15 (2012) #12.8.4.


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

Cf. A127670, A191092.
Sequence in context: A012112 A294435 A137246 * A324449 A191589 A194729
Adjacent sequences: A171857 A171858 A171859 * A171861 A171862 A171863


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Oct 16 2010


EXTENSIONS

Slightly edited by Gill Barequet, May 25 2011


STATUS

approved



