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 A208736 Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank level between 0 and 1. 2
 0, 0, 0, 1, 5, 22, 91, 361, 1392, 5265, 19653, 72694, 267179, 977593, 3565600, 12975457, 47142021, 171075606, 620303547, 2247803785, 8141857808, 29481675889, 106728951109, 386314552438, 1398132674955, 5059626441177, 18308871648576, 66249898660801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Uniform used in the sense of Retakh, Serconek and Wilson. We use Stanley's definition of graded poset: all maximal chains have the same length n (which also implies all maximal elements have maximal rank.) REFERENCES R. Stanley, Enumerative combinatorics. Vol. 1, Cambridge University Press, Cambridge, 1997, pp. 96-100. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 V. Retakh, S. Serconek, and R. Wilson, Hilbert Series of Algebras Associated to Directed Graphs and Order Homology, arXiv:1010.6295 [math.RA], 2010-2011. Wikipedia, Graded poset Index entries for linear recurrences with constant coefficients, signature (8,-21,20,-5). FORMULA a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4), a(2) = 0, a(3) = 1, a(4) = 5, a(5) = 22. G.f.: (x^3 - 3*x^4 + 3*x^5)/(1 - 8*x + 21*x^2 - 20*x^3 + 5*x^4); (x^3 * (1 - 3*x + 3*x^2))/((1 - 3*x + x^2)*(1 - 5*x + 5*x^2)) . a(n) = A081567(n-2) - A001519(n-1). MATHEMATICA Join[{0, 0}, LinearRecurrence[{8, -21, 20, -5}, {0, 1, 5, 22}, 40]] PROG (Python) def a(n, d={0:0, 1:0, 2:0, 3:1, 4:5, 5:22}):     if n in d:         return d[n]     d[n]=8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4)     return d[n] CROSSREFS Cf. A208737, A206901, A206902, A206947-A206950, A001906, A025192, A081567, A124302, A124292, A088305, A086405, A012781. Sequence in context: A128566 A097138 A105467 * A050185 A216597 A085812 Adjacent sequences:  A208733 A208734 A208735 * A208737 A208738 A208739 KEYWORD nonn,easy AUTHOR David Nacin, Mar 01 2012 STATUS approved

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Last modified July 3 18:04 EDT 2022. Contains 355055 sequences. (Running on oeis4.)