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 A206949 Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with no 3-element antichain. 4
 0, 0, 0, 3, 24, 135, 657, 2961, 12744, 53244, 218025, 880308, 3518721, 13961727, 55097091, 216546048, 848476296, 3316800555, 12942852624, 50437433079, 196347606849, 763752142233, 2969021213928, 11536374392820, 44809232564673, 173997851613660, 675501426136017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Here, the term uniform is 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. REFERENCES Richard P. 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 (9,-27,30,-9). FORMULA a(n) = 9*a(n-1) - 27*a(n-2) + 30*a(n-3) - 9*a(n-4), a(1)=0, a(2)=0, a(3)=3, a(4)=24. G.f.: (3*(1-x)*x^3)/((1-3*x)*(1-6*x+9*x^2-3*x^3)). a(n) = A124292(n+1) - A025192(n). MATHEMATICA Join[{0}, LinearRecurrence[{9, -27, 30, -9}, {0, 0, 3, 24}, 40]] PROG (Python) def a(n, adict={0:0, 1:0, 2:0, 3:3, 4:24}): .if n in adict: ..return adict[n] .adict[n]=9*a(n-1)-27*a(n-2)+30*a(n-3)-9*a(n-4) .return adict[n] CROSSREFS Cf. A206950 (maximal element removed). Cf. A206947, A206948 (requiring exactly two elements in each rank level above 0 with and without maximal element). Sequence in context: A183900 A001089 A069515 * A215636 A056350 A056344 Adjacent sequences:  A206946 A206947 A206948 * A206950 A206951 A206952 KEYWORD nonn,easy AUTHOR David Nacin, Feb 13 2012 STATUS approved

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Last modified August 14 09:14 EDT 2020. Contains 336480 sequences. (Running on oeis4.)