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

Author

David Nacin, Feb 21 2017

Keywords

• nonn
• easy

Comments

Also the number of inequivalent ways to color the corners of an octahedron using at most n colors so that no color appears more than twice.

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).

Crossrefs

Cf. A249460, A282816. A047780 (face colorings without restriction).

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