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 A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64. 3
 0, 0, 0, 0, 1, 1370, 738842, 176796382, 26021566536, 2807549333568, 245222809302240, 18418417704308160, 1236761946163054080, 76210520306627266560, 4388527139331858082560, 239214759548062858560000, 12457699161320493400320000, 623967599346727576292352000 (list; graph; refs; listen; history; text; internal format)
 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 V. Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set 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 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 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

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Last modified October 2 07:56 EDT 2023. Contains 365831 sequences. (Running on oeis4.)