A056073 Number of 7-element ordered antichains on an unlabeled n-element set; T_1-hypergraphs with 7 labeled nodes and n hyperedges.

20580, 9209340, 1113220168, 64271300556, 2302652531436, 59028678965286, 1179552813324360, 19421453010531722, 273692092058502488, 3392151018511583748, 37729265705269684476

Offset

5,1

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 and G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

Table of n, a(n) for n=5..15.

K. S. Brown, Dedekind's problem

Formula

a(n)=C(n + 127, 127) - 42*C(n + 95, 95) + 210*C(n + 79, 79) + 140*C(n + 71, 71) + 210*C(n + 67, 67) - 84*C(n + 65, 65) + 14*C(n + 64, 64) - 819*C(n + 63, 63) - 2520*C(n + 59, 59) + 2730*C(n + 55, 55) + 840*C(n + 53, 53) + 840*C(n + 51, 51) - 420*C(n + 50, 50) + 2940*C(n + 49, 49) + 630*C(n + 47, 47) - 5040*C(n + 45, 45) + 840*C(n + 44, 44) - 1260*C(n + 43, 43) +

1680*C(n + 42, 42) - 9660*C(n + 41, 41) + 1260*C(n + 40, 40) + 3360*C(n + 39, 39) - 7560*C(n + 38, 38) + 11130*C(n + 37, 37) + 5880*C(n + 36, 36) + 9240*C(n + 35, 35) + 2982*C(n + 34, 34) - 6300*C(n + 33, 33) - 8652*C(n + 32, 32) - 9905*C(n + 31, 31) - 8400*C(n + 30, 30) - 8540*C(n + 29, 29) + 13860*C(n + 28, 28) + 14490*C(n + 27, 27) - 5040*C(n + 26, 26) + 10500*C(n + 25, 25) +

10080*C(n + 24, 24) - 8120*C(n + 23, 23) - 15050*C(n + 22, 22) - 5040*C(n + 21, 21) - 11340*C(n + 20, 20) + 20580*C(n + 19, 19) + 15750*C(n + 18, 18) - 1540*C(n + 17, 17) - 5810*C(n + 16, 16) - 16485*C(n + 15, 15) - 21420*C(n + 14, 14) + 26250*C(n + 13, 13) + 21000*C(n + 12, 12) - 29820*C(n + 11, 11) + 3500*C(n + 10, 10) + 17640*C(n + 9, 9) + 2940*C(n + 8, 8) - 16016*C(n + 7, 7) + 4410*C(n + 6, 6) - 9744*C(n + 5, 5) + 9744*C(n + 4, 4) + 1764*C(n + 3, 3) - 3528*C(n + 2, 2) + 720*C(n + 1, 1).

Crossrefs

A051115 for 7-element (unordered) antichains on a labeled n-element set, A056005.

Sequence in context: A235587 A082254 A059050 * A173378 A028519 A247926

Adjacent sequences: A056070 A056071 A056072 * A056074 A056075 A056076

Keyword

nonn

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 26 2000

Status

approved