A059052 -id:A059052 - cp's OEIS frontend

A059081 Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32.

0, 0, 0, 0, 6, 2086, 273072, 19371912, 940055760, 35289051840, 1099827892800, 29723466326400, 716351882400000, 15683016533184000, 315722887044364800, 5890186860509952000, 102288867798813696000, 1656523525703574528000

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

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.

G. C. Greubel, Table of n, a(n) for n = 0..32
Vladeta Jovovic, Formula for the number of m-element T_0-antichains on a labeled n-set

Cf. A059079, A059080, A059082, A059083, A059048-A059052.

P[x_, n_] := (-1)^n*Pochhammer[-x, n]; Table[(1/5!)*(P[32, n] - 20*P[24, n] + 60*P[20, n] + 20*P[18, n] + 10*P[17, n] - 110*P[16, n] - 120*P[15, n] + 150*P[14, n] + 120*P[13, n] - 240*P[12, n] + 20*P[11, n] + 240*P[10, n] + 40*P[9, n] - 205*P[8, n] + 60*P[7, n] - 210*P[6, n] + 210*P[5, n] + 50*P[4, n] - 100*P[3, n] + 24*P[2, n]), {n, 0, 32}] (* G. C. Greubel, Oct 07 2017 *)

a(n) = (1/5!)*([32]_n - 20*[24]_n + 60*[20]_n + 20*[18]_n + 10*[17]_n - 110*[16]_n - 120*[15]_n + 150*[14]_n + 120*[13]_n - 240*[12]_n + 20*[11]_n + 240*[10]_n + 40*[9]_n - 205*[8]_n + 60*[7]_n - 210*[6]_n + 210*[5]_n + 50*[4]_n - 100*[3]_n + 24*[2]_n), where [k]_n := k*(k - 1)*...*(k - n + 1), [k]_0 = 1.

A059082 Number of 6-element T_0-antichains on a labeled n-set, n = 0, ..., 64.

Original entry on oeis.org

0, 0, 0, 0, 1, 1370, 738842, 176796382, 26021566536, 2807549333568, 245222809302240, 18418417704308160, 1236761946163054080, 76210520306627266560, 4388527139331858082560, 239214759548062858560000, 12457699161320493400320000, 623967599346727576292352000

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

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

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

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

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.

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

cp's OEIS Frontend

A059081 Number of 5-element T_0-antichains on a labeled n-set, n=0,..,32.

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