A011826 f-vectors for simplicial complexes of dimension at most 1 (graphs) on at most n-1 vertices.

2, 3, 5, 9, 16, 27, 43, 65, 94, 131, 177, 233, 300, 379, 471, 577, 698, 835, 989, 1161, 1352, 1563, 1795, 2049, 2326, 2627, 2953, 3305, 3684, 4091, 4527, 4993, 5490, 6019, 6581, 7177, 7808, 8475, 9179, 9921, 10702, 11523, 12385, 13289

Offset: 1

Author

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

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Aviezri S. Fraenkel and Urban Larsson, Playability and arbitrarily large rat games, arXiv:1705.03061 [math.CO], 2017. See p. 27.
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

Crossrefs

Cf. A000124, A004006, A014206, A033547.

Programs

Mathematica

a=2;s=3;lst={0,1,s};Do[a+=n;s+=a;AppendTo[lst,s],{n,2,4!,1}];lst+2 (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)

Formula

a(n) = (n^3 - 3n^2 + 8n + 6)/6 fits all listed terms. - John W. Layman, Mar 13 1999

Empirical G.f.: -x*(x^3 - 5*x^2 + 5*x - 2) / (x - 1)^4. - Colin Barker, Sep 19 2012