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

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%I A011826 #38 Jul 14 2023 15:12:36
%S A011826 2,3,5,9,16,27,43,65,94,131,177,233,300,379,471,577,698,835,989,1161,
%T A011826 1352,1563,1795,2049,2326,2627,2953,3305,3684,4091,4527,4993,5490,
%U A011826 6019,6581,7177,7808,8475,9179,9921,10702,11523,12385,13289
%N A011826 f-vectors for simplicial complexes of dimension at most 1 (graphs) on at most n-1 vertices.
%H A011826 Vincenzo Librandi, <a href="/A011826/b011826.txt">Table of n, a(n) for n = 1..1000</a>
%H A011826 Aviezri S. Fraenkel and Urban Larsson, <a href="https://arxiv.org/abs/1705.03061">Playability and arbitrarily large rat games</a>, arXiv:1705.03061 [math.CO], 2017. See p. 27.
%H A011826 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%F A011826 a(n) = (n^3 - 3n^2 + 8n + 6)/6 fits all listed terms. - _John W. Layman_, Mar 13 1999
%F A011826 Empirical G.f.: -x*(x^3 - 5*x^2 + 5*x - 2) / (x - 1)^4. - _Colin Barker_, Sep 19 2012
%t A011826 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 *)
%Y A011826 Cf. A000124, A004006, A014206, A033547.
%K A011826 nonn
%O A011826 1,1
%A A011826 Svante Linusson (linusson(AT)math.kth.se)