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%I #14 Sep 18 2012 16:44:37
%S 2,3,5,10,26,95,457,2246,9705,35926,115688,331201,859587,2054860,
%T 4582126,9627831,19217260,36679253,67308375,119286676,204940824,
%U 342425909,557944719,888630900,1386246251,2121866592,3191757298
%N Number of f-vectors for simplicial complexes of dimension at most 3 on at most n-1 vertices.
%D D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743).
%D S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
%F a(n+1) = (12*n^10 -112*n^9 +351*n^8 -132*n^7 +378*n^6 -2856*n^5 +4839*n^4 +56812*n^3 -5580*n^2 +309168*n +725760)/362880 fits terms up to 3191757298. [_Frank Ellermann_]
%F Empirical G.f.: -x*(x^10 -11*x^9 +69*x^8 -130*x^7 +380*x^6 -400*x^5 +356*x^4 -210*x^3 +82*x^2 -19*x +2)/(x -1)^11. [_Colin Barker_, Sep 18 2012]
%Y Cf. A011827, A007695.
%K nonn
%O 1,1
%A Svante Linusson (linusson(AT)math.kth.se)