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A097513
Number of ways to label the vertices of the octahedron (or faces of the cube) with nonnegative integers summing to n, where labelings that differ only by rotation or reflection are considered the same.
2
1, 1, 3, 5, 10, 15, 27, 38, 60, 84, 122, 164, 229, 298, 398, 509, 658, 823, 1041, 1278, 1582, 1917, 2331, 2786, 3343, 3948, 4676, 5471, 6408, 7428, 8622, 9912, 11406, 13023, 14871, 16866, 19135, 21571, 24321, 27275, 30580, 34122, 38070, 42284, 46956, 51942
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
Cf. A006381.
Sequence in context: A254346 A132302 A308872 * A308932 A308997 A045513
KEYWORD
easy,nonn
AUTHOR
Isabel C. Lugo (izzycat(AT)gmail.com), Aug 26 2004
STATUS
approved