A282816 Number of inequivalent ways to color the faces of a cube using at most n colors so that no two opposite sides have the same color.

0, 0, 1, 11, 76, 340, 1135, 3101, 7336, 15576, 30405, 55495, 95876, 158236, 251251, 385945, 576080, 838576, 1193961, 1666851, 2286460, 3087140, 4108951, 5398261, 7008376, 9000200, 11442925, 14414751, 18003636, 22308076, 27437915, 33515185, 40674976, 49066336

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 two opposite corners have the same color.

Examples

			For n = 2 we get a(2) = 1 way to color the faces of a cube with two colors so that no two opposite sides have the same color.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A282817, A047780 (face colorings without restriction).

Programs

Mathematica

Table[(8n(n-1) + n^3(n-1)^3) /24, {n, 0, 35}]

PARI

a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24 \\ Charles R Greathouse IV, Feb 22 2017

Formula

a(n) = n*(n-1)*(n^4-2*n^3+n^2+8)/24.

G.f.: -x^2*(1+4*x+20*x^2+4*x^3+x^4)/(x-1)^7 . - R. J. Mathar, Feb 23 2017