cp's OEIS Frontend

A206901 Number of nonisomorphic graded posets with 0 of rank n with no 3-element antichain.

%I A206901 #38 May 17 2021 08:49:07
%S A206901 1,2,8,39,199,1027,5316,27539,142694,739416,3831589,19855045,
%T A206901 102887673,533158028,2762794601,14316644946,74188042696,384438233215,
%U A206901 1992137140383,10323141778619,53493935746148,277202543857995,1436447874880342,7443591492820888
%N A206901 Number of nonisomorphic graded posets with 0 of rank n with no 3-element antichain.
%C A206901 We do not assume all maximal elements have maximal rank and thus use graded poset to mean: For every element x, all maximal chains among those with x as greatest element have the same finite length.
%H A206901 Vincenzo Librandi, <a href="/A206901/b206901.txt">Table of n, a(n) for n = 0..1000</a>
%H A206901 Vladimir Retakh, Shirlei Serconek, and Robert Wilson, <a href="http://arxiv.org/abs/1010.6295">Hilbert series of algebras associated to direct graphs and order homology</a>, arXiv 1010.6295 [math.RA], 2010-2011.
%H A206901 Wikipedia, <a href="http://en.wikipedia.org/wiki/Graded_poset">Graded poset</a>
%H A206901 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10,3).
%F A206901 a(n+3) = 7a(n+2) - 10a(n+1) + 3a(n), a(0)=1, a(1)=2, a(2)=8.
%F A206901 G.f.: (1-5x+4x^2)/(1-7x+10x^2-3x^3).
%t A206901 m = {{3, 3, 1, 0}, {1, 3, 0, 0}, {2, 3, 1, 0}, {6, 9, 2, 0}}; Table[MatrixPower[m, n][[4,3]], {n, 1, 40}]
%o A206901 (Python)
%o A206901 def a(n,adict={0:1,1:2,2:8}):
%o A206901     if n in adict:
%o A206901         return adict[n]
%o A206901     adict[n]=7*a(n-1)-10*a(n-2)+3*a(n-3)
%o A206901     return adict[n]
%Y A206901 Cf. A124292 (counts with unique maximal element).
%Y A206901 Cf. A025192, A206902 (adding a uniformity condition in the sense of the Retakh et al. paper with and without maximal elements).
%K A206901 nonn,easy
%O A206901 0,2
%A A206901 _David Nacin_, Feb 13 2012