A011826 - OEIS

%I #38 Jul 14 2023 15:12:36

%S 2,3,5,9,16,27,43,65,94,131,177,233,300,379,471,577,698,835,989,1161,

%T 1352,1563,1795,2049,2326,2627,2953,3305,3684,4091,4527,4993,5490,

%U 6019,6581,7177,7808,8475,9179,9921,10702,11523,12385,13289

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

%H Vincenzo Librandi, <a href="/A011826/b011826.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 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 a(n) = (n^3 - 3n^2 + 8n + 6)/6 fits all listed terms. - _John W. Layman_, Mar 13 1999

%F Empirical G.f.: -x*(x^3 - 5*x^2 + 5*x - 2) / (x - 1)^4. - _Colin Barker_, Sep 19 2012

%t 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 Cf. A000124, A004006, A014206, A033547.

%K nonn

%O 1,1

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