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 color appears more than twice.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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
EXAMPLE
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.
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Nacin, Feb 21 2017
STATUS
approved