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
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
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 21 2017
STATUS
approved