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

0, 1, 214, 21225, 1688424, 125055400, 9178531200, 687848686448, 53435249786880, 4336107249936384, 368887991492608000, 32948013484980000000, 3090086319932923969536, 304136142049322287011840, 31382704663810285705887744, 3390841628447041935421747200, 383124440688361472000000000000

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