%I A097513
%S A097513 1,1,3,5,10,15,27,38,60,84,122,164,229,298,398,509,658,823,1041,1278,
%T A097513 1582,1917,2331,2786,3343,3948,4676,5471,6408,7428,8622,9912,11406,
%U A097513 13023,14871,16866,19135,21571,24321,27275
%N 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.
%F A097513 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))
%F A097513 a(n) is asymptotically equal to n^5/5760. - Isabel C. Lugo (izzycat(AT)gmail.com), 
               Aug 31 2004
%e A097513 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.
%p A097513 (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]
%Y A097513 Cf. A006381.
%Y A097513 Sequence in context: A126728 A070557 A132302 this_sequence A045513 A008337 
               A077285
%Y A097513 Adjacent sequences: A097510 A097511 A097512 this_sequence A097514 A097515 
               A097516
%K A097513 easy,nonn
%O A097513 0,3
%A A097513 Isabel C. Lugo (izzycat(AT)gmail.com), Aug 26 2004