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A059082
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Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.
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3
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0, 0, 0, 0, 1, 1370, 738842, 176796382, 26021566536, 2807549333568, 245222809302240, 18418417704308160, 1236761946163054080, 76210520306627266560, 4388527139331858082560, 239214759548062858560000, 12457699161320493400320000, 623967599346727576292352000
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OFFSET
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0,6
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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FORMULA
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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.
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MAPLE
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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
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CROSSREFS
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KEYWORD
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nonn,easy,fini,full
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AUTHOR
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 06 2005
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STATUS
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approved
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