A282817 Number of inequivalent ways to color the faces of a cube using at most n colors so that no color appears more than twice.
0, 0, 0, 6, 72, 375, 1320, 3675, 8736, 18522, 36000, 65340, 112200, 184041, 290472, 443625, 658560, 953700, 1351296, 1877922, 2565000, 3449355, 4573800, 5987751, 7747872, 9918750, 12573600, 15795000, 19675656, 24319197, 29841000, 36369045, 44044800, 53024136
Offset: 0
Examples
For n=3 we get a(3)=6 ways to color the faces of a cube with three colors so that no color appears more than twice.
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
-
Mathematica
Table[(3 n (n - 1) (n - 2)^2 + 6 n (n - 1) (n - 2) + n (n - 1) (n - 2) (n - 3) (n - 4) (n - 5) + 15 n (n - 1) (n - 2) (n - 3) (n - 4) + 45 n (n - 1) (n - 2) (n - 3) + 15 n (n - 1) (n - 2))/24, {n, 0, 16}]
Formula
a(n) = (n-2)^2*(n-1)*n^2*(n+5)/24.
G.f.: 3*x^3*(-2-10*x+x^2+x^3)/(x-1)^7 . - R. J. Mathar, Feb 23 2017
Comments