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%I #38 Sep 08 2022 08:45:50
%S 0,1,17,348,8640,254800,8749056,343901376,15257600000,755110160640,
%T 41278242816000,2471677136321536,160961785787056128,
%U 11330322120000000000,857485369051342438400,69444841895469240729600,5993559601317659925282816,549242871950650346384195584
%N Number of n-cell fixed polycubes that are proper in n-2 dimensions.
%D 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
%D 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.
%D R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of high-dimensional polycubes, Combinatorica, 30 (2010), 257-275. See Th. 6.
%H Vincenzo Librandi, <a href="/A171860/b171860.txt">Table of n, a(n) for n = 2..100</a>
%H A. Asinowski, G. Barequet, R. Barequet, and G. Rote, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Barequet/barequet2.html">Proper n-Cell Polycubes in n-3 Dimensions</a>, J. Int. Seq. 15 (2012) #12.8.4.
%H M. Shalah, <a href="http://www.cs.technion.ac.il/~barequet/theses/shalah-phd-thesis.pdf">Formulae and growth rates of animals on cubical and triangular lattices</a>, PhD Thesis, Israel Inst. Techn. (2017).
%F a(n) = 2^(n-3)*n^(n-5)*(n-2)*(2*n^2 - 6*n + 9).
%o (Magma) [2^(n-3)*n^(n-5)*(n-2)*(2*n^2-6*n+9): n in [2..20]]; // _Vincenzo Librandi_, May 26 2011
%Y Cf. A127670, A191092, A036364 (free).
%Y Diagonal 2 of A195739.
%K nonn
%O 2,3
%A _N. J. A. Sloane_, Oct 16 2010
%E Slightly edited by _Gill Barequet_, May 25 2011
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