|
%I #25 Apr 16 2018 11:13:29
%S 1,2,5,14,40,121,373,1184,3823,12554,41733,140301,475934,1627440,
%T 5602983,19406703,67574371,236409625,830582851,2929246932,10366380583,
%U 36801225872,131021870786,467701875135,1673584553886,6002046468815,21570135722058,77668429499325,280167079428684,1012323004985313
%N Number of N- and bowtie-free posets with n elements.
%C The number of n-element posets that do not include the two 4-element posets "N" and "bowtie" as induced subposets.
%H Stephan Wagner, <a href="/A301871/b301871.txt">Table of n, a(n) for n = 1..100</a>
%H T. Hasebe and S. Tsujie, <a href="https://arxiv.org/abs/1610.03908">Order quasisymmetric functions distinguish rooted trees</a>, arXiv:1610.03908 [math.CO], 2016-2017.
%H T. Hasebe and S. Tsujie, <a href="https://doi.org/10.1007/s10801-017-0761-7">Order quasisymmetric functions distinguish rooted trees</a>, Journal of Algebraic Combinatorics 46 (2017), 499-515.
%H V. Razanajatovo Misanantenaina and S. Wagner, <a href="https://arxiv.org/abs/1803.09623">A Tutte-like polynomial for rooted trees and specific posets</a>, arXiv:1803.09623 [math.CO], 2018.
%F G.f. V(x) = 1 + x + 2x + 5x^2 + ... satisfies V(x) = (1-x)exp[sum_{m >=1} (2x^m-x^(2m))V(x^m)/m] (see Razanajatovo Misanantenaina/Wagner).
%t V=1;Do[V = Normal[Series[(1 - x) Exp[Sum[(2 x^m - x^(2 m)) (V /. x -> x^m)/m, {m, 1, n}]], {x, 0, n}]], {n, 1, 20}]; Table[Coefficient[V,x,n],{n, 1, 20}]
%Y Cf. A000112, A003430, A079144, A079146 for related sequences regarding the enumeration of unlabeled posets.
%K nonn,easy
%O 1,2
%A _Stephan Wagner_, Mar 28 2018
|
