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 A056069 Number of 4-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 4 labeled nodes and n hyperedges. 4
 25, 454, 3818, 21420, 92805, 335152, 1055944, 2990020, 7767357, 18789070, 42797602, 92588216, 191542842, 381000192, 731941256, 1363109096, 2468549141, 4358716470, 7520830306, 12706161124, 21054530855, 34269633840, 54863015040, 86489873580, 134406530985 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS T_1-hypergraph is a hypergraph (not necessarily without empty hyperedges or multiple hyperedges) which for every ordered pair of distinct nodes has a hyperedge containing one but not the other node. REFERENCES V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6) V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation. LINKS T. D. Noe, Table of n, a(n) for n = 4..1000 K. S. Brown, Dedekind's problem FORMULA a(n) = C(n + 15, 15) - 12*C(n + 11, 11) + 24*C(n + 9, 9) + 4*C(n + 8, 8) - 18*C(n + 7, 7) + 6*C(n + 6, 6) - 36*C(n + 5, 5) + 36*C(n + 4, 4) + 11*C(n + 3, 3) - 22*C(n + 2, 2) + 6*C(n + 1, 1). Empirical G.f.: x^4*(6*x^10 -62*x^9 +271*x^8 -636*x^7 +800*x^6 -328*x^5 -495*x^4 +812*x^3 -446*x^2 +54*x +25)/(x-1)^16. [Colin Barker, May 29 2012] CROSSREFS Cf. A051112 for 4-element (unordered) antichains on a labeled n-element set, A056005. Sequence in context: A016633 A001811 A131279 * A089386 A014927 A059946 Adjacent sequences:  A056066 A056067 A056068 * A056070 A056071 A056072 KEYWORD nonn AUTHOR Vladeta Jovovic, Goran Kilibarda, Jul 26 2000 STATUS approved

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Last modified January 19 12:28 EST 2022. Contains 350465 sequences. (Running on oeis4.)