cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A059083 Number of T_0-antichains on a labeled n-set.

Original entry on oeis.org

2, 3, 3, 8, 96, 6373, 7725703, 2414518872815, 56130437161078967568912
Offset: 0

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Author

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

Keywords

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.

Examples

			a(0) = 1 + 1, a(1) = 1 + 2, a(2) = 2 + 1, a(3) = 6 + 2, a(4) = 12 + 52 + 25 + 6 + 1, a(5) = 520 + 1770 + 2086 + 1370 + 490 + 115 + 20 + 2.
		

References

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

Crossrefs

Formula

a(n) = Sum_{m=0..binomial(n, floor(n/2))} A(m, n), where A(m, n) is number of m-element T_0-antichains on a labeled n-set. Cf. A059080.
a(n) = column sums of A059080.

Extensions

More terms from Vladeta Jovovic, Nov 28 2003

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

Original entry on oeis.org

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

Views

Author

Vladeta Jovovic, Goran Kilibarda, Jan 06 2001

Keywords

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.

Crossrefs

Programs

  • Mathematica
    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 *)

Formula

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.
Showing 1-2 of 2 results.