A005745 Number of n-covers of an unlabeled 3-set.

1, 6, 23, 65, 156, 336, 664, 1229, 2159, 3629, 5877, 9221, 14070, 20951, 30530, 43634, 61283, 84725, 115461, 155294, 206368, 271210, 352784, 454550, 580509, 735280, 924163, 1153207, 1429292, 1760218, 2154776, 2622859, 3175555, 3825247

Offset: 1

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• easy
• nonn

Comments

Number of n X 3 binary matrices with at least one 1 in every column up to row and column permutations. - Andrew Howroyd, Feb 28 2023

References

• R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• Vladeta Jovovic, Binary matrices up to row and column permutations

Crossrefs

A diagonal of A055080.

First differences give A055609.

Cf. A002623, A002727.

Cf. A005744, A005746, A005747, A005748, A005771.

Programs

PARI

Vec(G(3, x) - G(2, x) + O(x^40)) \\ G defined in A028657. - Andrew Howroyd, Feb 28 2023

Formula

a(n) = A002727(n) - A002623(n).

G.f.: -x*(x^8-x^7-x^6-2*x^5+2*x^4+x^3-3*x^2-2*x-1)/((x^3-1)^2*(x^2-1)^2*(x-1)^4).

Extensions

More terms from Vladeta Jovovic, May 26 2000