OFFSET
0,6
COMMENTS
An antichain on a set is a T_0-antichain if for every two distinct points of the set there exists a member of the antichain containing one but not the other point.
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
Alois P. Heinz, Table of n, a(n) for n = 0..64
FORMULA
a(n) = (1/6!)*([64]_n - 30*[48]_n + 120*[40]_n + 60*[36]_n + 60*[34]_n - 12*[33]_n - 345*[32]_n - 720*[30]_n + 810*[28]_n + 120*[27]_n + 480*[26]_n + 360*[25]_n - 480*[24]_n - 720*[23]_n - 240*[22]_n - 540*[21]_n + 1380*[20]_n + 750*[19]_n + 60*[18]_n - 210*[17]_n - 1535*[16]_n - 1820*[15]_n + 2250*[14]_n + 1800*[13]_n - 2820*[12]_n + 300*[11]_n + 2040*[10]_n + 340*[9]_n - 1815*[8]_n + 510*[7]_n - 1350*[6]_n + 1350*[5]_n + 274*[4]_n - 548*[3]_n + 120*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.
MAPLE
f:=proc(k, n) if k+1<=n then RETURN(0) else RETURN(k!/(k - n)!) fi: end; a:=n->(1/6!)*(f(64, n) - 30*f(48, n) + 120*f(40, n) + 60*f(36, n) + 60*f(34, n)- 12*f(33, n) - 345*f(32, n) - 720*f(30, n) + 810*f(28, n) + 120*f(27, n) + 480*f(26, n) + 360*f(25, n) - 480*f(24, n) - 720*f(23, n) - 240*f(22, n) - 540*f(21, n) + 1380*f(20, n) + 750*f(19, n) + 60*f(18, n) - 210*f(17, n) - 1535*f(16, n) - 1820*f(15, n) + 2250*f(14, n) + 1800*f(13, n) - 2820*f(12, n) + 300*f(11, n) + 2040*f(10, n) + 340*f(9, n) - 1815*f(8, n) + 510*f(7, n) - 1350*f(6, n) + 1350*f(5, n) + 274*f(4, n) - 548*f(3, n) + 120*f(2, n)); seq(a(n), n=0..20); # Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
CROSSREFS
KEYWORD
nonn,easy,fini,full
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jan 06 2001
EXTENSIONS
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
STATUS
approved