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 A259015 The number of fixed polycubes of size n that span n-4 dimensions. 5
 0, 1, 214, 21225, 1688424, 125055400, 9178531200, 687848686448, 53435249786880, 4336107249936384, 368887991492608000, 32948013484980000000, 3090086319932923969536, 304136142049322287011840, 31382704663810285705887744, 3390841628447041935421747200, 383124440688361472000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 REFERENCES 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 4..351 G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes (video) G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes (pdf file) FORMULA 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. MATHEMATICA 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 *) PROG (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 (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 CROSSREFS Diagonal 4 of A195739. Sequence in context: A200043 A184600 A278093 * A207279 A207475 A207531 Adjacent sequences: A259012 A259013 A259014 * A259016 A259017 A259018 KEYWORD nonn,easy AUTHOR Mira Shalah, Jun 16 2015 EXTENSIONS Typo in formula fixed by Colin Barker, Jun 16 2015 STATUS approved

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Last modified May 22 06:48 EDT 2024. Contains 372743 sequences. (Running on oeis4.)