0,6

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.

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.

Alois P. Heinz, Table of n, a(n) for n = 0..64

V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

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.

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

Cf. A059079, A059080, A059081, A059083, A059048, A059049, A059050, A059051, A059052.

Sequence in context: A031662 A251567 A251562 * A178485 A031535 A031715

Adjacent sequences: A059079 A059080 A059081 * A059083 A059084 A059085

nonn,easy,fini,full

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005

approved