OFFSET
0,3
FORMULA
G.f.: (q^8-q^7+q^6+q^4+q^2-q+1)/((-1+q)^6*(q+1)^3*(q^2+q+1)^2*(q^2-q+1)*(q^2+1)).
a(n) is asymptotically equal to n^5/5760. - Isabel C. Lugo (izzycat(AT)gmail.com), Aug 31 2004
EXAMPLE
a(3) = 5 because we can label the faces of the cube with nonnegative integers summing to three in five ways: 3 on one face, 2 on one face and 1 on an adjacent face, 2 on one face and 1 on the opposite face, 1 on three faces sharing a corner, 1 on three faces not sharing a corner.
MAPLE
a:= n-> (Matrix([[1, 0$8, -1$2, -3, -5, -10, -15, -27, -38]]).Matrix(17, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 0, -1, 0, -2, 3, -2, 1, 1, -2, 3, -2, 0, -1, 0, 2, -1][i] else 0 fi)^n)[1, 1]; seq(a(n), n=0..50); # Alois P. Heinz, Jul 31 2008
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Isabel C. Lugo (izzycat(AT)gmail.com), Aug 26 2004
STATUS
approved