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A097513
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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.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Generating function: (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
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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.
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MAPLE
| (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..39); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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CROSSREFS
| Cf. A006381.
Sequence in context: A126728 A070557 A132302 * A045513 A008337 A077285
Adjacent sequences: A097510 A097511 A097512 * A097514 A097515 A097516
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KEYWORD
| easy,nonn
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AUTHOR
| Isabel C. Lugo (izzycat(AT)gmail.com), Aug 26 2004
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