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

0,4

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.

Links

Table of n, a(n) for n=0..33.

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A287330 A282384 A092225 * A055901 A036427 A122589

Adjacent sequences: A282813 A282814 A282815 * A282817 A282818 A282819

Keyword

nonn,easy

Author

David Nacin, Feb 21 2017

Status

approved