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 A206901 Number of nonisomorphic graded posets with 0 of rank n with no 3-element antichain. 5
 1, 2, 8, 39, 199, 1027, 5316, 27539, 142694, 739416, 3831589, 19855045, 102887673, 533158028, 2762794601, 14316644946, 74188042696, 384438233215, 1992137140383, 10323141778619, 53493935746148, 277202543857995, 1436447874880342, 7443591492820888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Vladimir Retakh, Shirlei Serconek, and Robert Wilson, Hilbert series of algebras associated to direct graphs and order homology, arXiv 1010.6295 [math.RA], 2010-2011. Wikipedia, Graded poset Index entries for linear recurrences with constant coefficients, signature (7,-10,3). FORMULA a(n+3) = 7a(n+2) - 10a(n+1) + 3a(n), a(0)=1, a(1)=2, a(2)=8. G.f.: (1-5x+4x^2)/(1-7x+10x^2-3x^3). MATHEMATICA 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}] PROG (Python) def a(n, adict={0:1, 1:2, 2:8}): if n in adict: return adict[n] adict[n]=7*a(n-1)-10*a(n-2)+3*a(n-3) return adict[n] CROSSREFS Cf. A124292 (counts with unique maximal element). Cf. A025192, A206902 (adding a uniformity condition in the sense of the Retakh et al. paper with and without maximal elements). Sequence in context: A154133 A077324 A112737 * A162476 A366049 A218321 Adjacent sequences: A206898 A206899 A206900 * A206902 A206903 A206904 KEYWORD nonn,easy AUTHOR David Nacin, Feb 13 2012 STATUS approved

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Last modified September 7 12:32 EDT 2024. Contains 375730 sequences. (Running on oeis4.)