cp's OEIS Frontend

A259015 The number of fixed polycubes of size n that span n-4 dimensions.

%I A259015 #36 Sep 08 2022 08:46:13
%S A259015 0,1,214,21225,1688424,125055400,9178531200,687848686448,
%T A259015 53435249786880,4336107249936384,368887991492608000,
%U A259015 32948013484980000000,3090086319932923969536,304136142049322287011840,31382704663810285705887744,3390841628447041935421747200,383124440688361472000000000000
%N A259015 The number of fixed polycubes of size n that span n-4 dimensions.
%D A259015 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.
%H A259015 Charles R Greathouse IV, <a href="/A259015/b259015.txt">Table of n, a(n) for n = 4..351</a>
%H A259015 G. Barequet and M. Shalah, <a href="https://www.youtube.com/watch?v=ojNDm8qKr9A">Automatic Proofs for Formulae Enumerating Proper Polycubes</a> (video)
%H A259015 G. Barequet and M. Shalah, <a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.19">Automatic Proofs for Formulae Enumerating Proper Polycubes</a> (pdf file)
%F A259015 a(n) = 2^(n-7)*n^(n-9)*(n-4)*(8*n^8 - 128*n^7 + 828*n^6 - 2930*n^5 + 7404*n^4 - 17523*n^3 + 41527*n^2 - 114302*n + 204960)/6.
%t A259015 Table[2^(n - 7) n^(n - 9) (n - 4) (8 n^8 - 128 n^7 + 828 n^6 - 2930 n^5 + 7404 n^4 - 17523 n^3 + 41527 n^2 - 114302 n + 204960)/6, {n, 4, 20}] (* _Michael De Vlieger_, Jun 19 2015 *)
%o A259015 (PARI) a(n)=2^(n-7)*n^(n-9)*(n-4)*(8*n^8-128*n^7+828*n^6 -2930*n^5 +7404*n^4-17523*n^3 +41527*n^2-114302*n +204960)/6 \\ _Charles R Greathouse IV_, Jun 16 2015
%o A259015 (Magma) [2^(n-7)*n^(n-9)*(n-4)*(8*n^8-128*n^7+828*n^6-2930*n^5 +7404*n^4-17523*n^3+41527*n^2-114302*n+204960)/6: n in [4..20]]; // _Vincenzo Librandi_, Jun 20 2015
%Y A259015 Diagonal 4 of A195739.
%K A259015 nonn,easy
%O A259015 4,3
%A A259015 _Mira Shalah_, Jun 16 2015
%E A259015 Typo in formula fixed by _Colin Barker_, Jun 16 2015