|
| |
|
|
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)).
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| Row sums give A000372.
|
|
|
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
| K. S. Brown, Dedekind's Problem
|
|
|
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 * A127772 A086256 A057550
Adjacent sequences: A059116 A059117 A059118 * A059120 A059121 A059122
|
|
|
KEYWORD
| nonn,tabf
|
|
|
AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jan 06 2001
|
| |
|
|
