A056069 Number of 4-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 4 labeled nodes and n hyperedges.

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

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