cp's OEIS Frontend

A206947 Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank above 0.

%I A206947 #38 May 17 2021 08:49:14
%S A206947 0,0,0,2,14,70,306,1248,4888,18666,70110,260414,959882,3519232,
%T A206947 12854064,46824210,170243566,618125238,2242100898,8126927456,
%U A206947 29442587720,106626616954,386046638142,1397431266222,5057790129274,18304064121600,66237312391776
%N A206947 Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank above 0.
%C A206947 Here, the term uniform used in the sense of Retakh, Serconek and Wilson.  Graded is used in terms of Stanley's definition that all maximal chains have the same length n.
%D A206947 R. Stanley, Enumerative combinatorics, Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100.
%H A206947 V. Retakh, S. Serconek, and R. Wilson, <a href="http://arxiv.org/abs/1010.6295">Hilbert Series of Algebras Associated to Directed Graphs and Order Homology</a>, arXiv:1010.6295 [math.RA], 2010-2011.
%H A206947 Wikipedia, <a href="http://en.wikipedia.org/wiki/Graded_poset">Graded poset</a>
%H A206947 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,20,-5).
%F A206947 a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4), a(1)=0, a(2)=0, a(3)=2, a(4)=14.
%F A206947 G.f.: (2*(1-x)*x^3)/((1-3*x+x^2)*(1-5*x+5*x^2)).
%F A206947 a(n) = A081567(n-1) - A001906(n).
%t A206947 Join[{0}, LinearRecurrence[{8, -21, 20, -5}, {0, 0, 2, 14}, 40]]
%o A206947 (Python)
%o A206947 def a(n,adict={0:0,1:0,2:0,3:2,4:14}):
%o A206947     if n in adict:
%o A206947         return adict[n]
%o A206947     adict[n]=8*a(n-1)-21*a(n-2)+20*a(n-3)-5*a(n-4)
%o A206947     return adict[n]
%Y A206947 Cf. A206948 (removing unique maximal element.)
%Y A206947 Cf. A206949, A206950 (allowing one or two elements in each rank level above 0 with and without maximal element.)
%K A206947 nonn,easy
%O A206947 0,4
%A A206947 _David Nacin_, Feb 13 2012