A059119 Triangle a(n,m)=number of m-element antichains on a labeled n-set; number of monotone n-variable Boolean functions with m mincuts (lower units), m=0..binomial(n,floor(n,2)).

1, 1, 1, 2, 1, 4, 1, 1, 8, 9, 2, 1, 16, 55, 64, 25, 6, 1, 1, 32, 285, 1090, 2020, 2146, 1380, 490, 115, 20, 2, 1, 64, 1351, 14000, 82115, 304752, 759457, 1308270, 1613250, 1484230, 1067771, 635044, 326990, 147440, 57675, 19238, 5325, 1170, 190, 20, 1, 1

Offset

0,4

Comments

Row sums give A000372.

References

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

Links

Suresh Govindarajan and Deepak Aditya, Table of n, a(n) for n = 0..94

K. S. Brown, Dedekind's Problem

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).

Formula

a(n, 0) = 1; a(n, 1) = 2^n; a(n, 2) = A016269(n); a(n, 3) = A047707(n); a(n, 4) = A051112(n); a(5, n) = A051113(n); a(6, n) = A051114(n); a(7, n) = A051115(n); a(8, n) = A051116(n); a(9, n) = A051117(n); a(10, n) = A051118(n).

Example

[1, 1],
[1, 2],
[1, 4, 1],
[1, 8, 9, 2],
[1, 16, 55, 64, 25, 6, 1],
[1, 32, 285, 1090, 2020, 2146, 1380, 490, 115, 20, 2], ...

Crossrefs

Cf. A000372, A016269, A047707, A051112-A051118.

Sequence in context: A137710 A068009 A140168 * A305333 A127772 A086256

Adjacent sequences: A059116 A059117 A059118 * A059120 A059121 A059122

Keyword

nonn,tabf

Author

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

Status

approved