A171860 Number of n-cell fixed polycubes that are proper in n-2 dimensions.

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

Offset: 2

Author

N. J. A. Sloane, Oct 16 2010

Keywords

• nonn

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. 19-22, 2015.
• R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica, 30 (2010), 257-275. See Th. 6.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..100
• A. Asinowski, G. Barequet, R. Barequet, and G. Rote, Proper n-Cell Polycubes in n-3 Dimensions, J. Int. Seq. 15 (2012) #12.8.4.
• M. Shalah, Formulae and growth rates of animals on cubical and triangular lattices, PhD Thesis, Israel Inst. Techn. (2017).

Crossrefs

Cf. A127670, A191092, A036364 (free).

Diagonal 2 of A195739.

Programs

Magma

[2^(n-3)*n^(n-5)*(n-2)*(2*n^2-6*n+9): n in [2..20]]; // Vincenzo Librandi, May 26 2011

Mathematica

Table[2^(n-3)n^(n-5)(n-2)(2n^2-6n+9),{n,2,30}] (* Harvey P. Dale, Nov 27 2024 *)

Formula

a(n) = 2^(n-3)*n^(n-5)*(n-2)*(2*n^2 - 6*n + 9).

Extensions

Slightly edited by Gill Barequet, May 25 2011