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 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

%I

%S 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,

%T 490,115,20,2,1,64,1351,14000,82115,304752,759457,1308270,1613250,

%U 1484230,1067771,635044,326990,147440,57675,19238,5325,1170,190,20,1,1

%N 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)).

%C Row sums give A000372.

%D 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)

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

%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath030.htm">Dedekind's Problem</a>

%F 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).

%e [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], ...

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

%K nonn,tabf,changed

%O 0,4

%A _Vladeta Jovovic_, Goran Kilibarda, Jan 06 2001

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Last modified June 19 16:00 EDT 2013. Contains 226414 sequences.