A059050 -id:A059050 - cp's OEIS frontend

A059052 Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.

2, 4, 4, 72, 38040, 4020463392, 18438434825136728352, 340282363593610211921722192165556850240, 115792089237316195072053288318104625954343609704705784618785209431974668731584

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

nonn

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. T_1-hypergraph is a hypergraph which for every ordered pair (u,v) of distinct nodes has a hyperedge containing u but not v.

			a(3) = 2 + 13 + 26 + 22 + 8 + 1. a(6) = 2^64 - 30*2^48 + 120*2^40 + 60*2^36 + 60*2^34 - 12*2^33 - 345*2^32 - 720*2^30 + 810*2^28 + 120*2^27 + 480*2^26 + 360*2^25 - 480*2^24 - 720*2^23 - 240*2^22 - 540*2^21 + 1380*2^20 + 750*2^19 + 60*2^18 - 210*2^17 - 1535*2^16 - 1820*2^15 + 2250*2^14 + 1800*2^13 - 2820*2^12 + 300*2^11 + 2040*2^10 + 340*2^9 - 1815*2^8 + 510*2^7 - 1350*2^6 + 1350*2^5 + 274*2^4 - 548*2^3 + 120*2^2.

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, in Russian, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, English translation, in Discrete Mathematics and Applications, 9, (1999), no. 6.

Cf. A059048, A059049, A059050, A059051, A326960.

a(n) = Sum_{m=0..2^n} A(n, m), where A(n, m) is number of n-element ordered T_0-antichains on an unlabeled m-set. Cf. A059048.

a(n) = row sums of A059048.

A059049 Number of 6-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 6 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,64).

Original entry on oeis.org

0, 0, 0, 0, 30, 8220, 738842, 25256626, 464670831, 5570534392, 48655319306, 332222541564, 1859009659336, 8811850222304, 36244568422086, 131710639199900, 428697293437675, 1263065928235140, 3396450715952370

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

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.

Sean A. Irvine, Table of n, a(n) for n = 0..64

Cf. A059048, A059050-A059052.

a(n)=C(64, n) - 30*C(48, n) + 120*C(40, n) + 60*C(36, n) + 60*C(34, n) - 12*C(33, n) - 345*C(32, n) - 720*C(30, n) + 810*C(28, n) + 120*C(27, n) + 480*C(26, n) + 360*C(25, n) - 480*C(24, n) - 720*C(23, n) - 240*C(22, n) - 540*C(21, n) + 1380*C(20, n) + 750*C(19, n) + 60*C(18, n) - 210*C(17, n) - 1535*C(16, n) - 1820*C(15, n) + 2250*C(14, n) + 1800*C(13, n) - 2820*C(12, n) + 300*C(11, n) + 2040*C(10, n) + 340*C(9, n) - 1815*C(8, n) + 510*C(7, n) - 1350*C(6, n) + 1350*C(5, n) + 274*C(4, n) - 548*C(3, n) + 120*C(2, n).

A059051 Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessarily empty) distinct hyperedges.

Original entry on oeis.org

2, 3, 2, 4, 99, 190866

Offset: 0

Vladeta Jovovic, Goran Kilibarda, Dec 19 2000

			a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 1 + 1, a(3) = 2 + 2, a(4) = 1 + 13 + 25 + 30 + 30, a(5) = 26 + 354 + 2086 + 8220 + 20580 + 38640 + 60480 + 60480.

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.
V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

Cf. A059048-A059050, A059052.

a(n) = Sum_{m=0..C(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element ordered T_0-antichains on an unlabeled n-set. Cf. A059048.

a(n) = column sums of A059048.

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

A059052 Number of n-element unlabeled ordered T_0-antichains; T_1-hypergraphs (with empty hyperedge but without multiple hyperedges) on n labeled nodes.

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A059049 Number of 6-element ordered T_0-antichains on an unlabeled n-set; T_1-hypergraphs on 6 labeled nodes with n (not necessarily empty) distinct hyperedges (n=0,1,...,64).

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A059051 Number of ordered T_0-antichains on an unlabeled n-set; labeled T_1-hypergraphs with n (not necessarily empty) distinct hyperedges.

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

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