A011828 Number of f-vectors for simplicial complexes of dimension at most 3 on at most n-1 vertices.

2, 3, 5, 10, 26, 95, 457, 2246, 9705, 35926, 115688, 331201, 859587, 2054860, 4582126, 9627831, 19217260, 36679253, 67308375, 119286676, 204940824, 342425909, 557944719, 888630900, 1386246251, 2121866592, 3191757298

Offset: 1

Author

Svante Linusson (linusson(AT)math.kth.se)

Keywords

• nonn

References

• D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743).
• S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.

Crossrefs

Cf. A011827, A007695.

Formula

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]

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]