A005745 Number of n-covers of an unlabeled 3-set. (Formerly M4156)

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

1,2

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

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).

Prog

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

Crossrefs

A diagonal of A055080.

First differences give A055609.

Cf. A002623, A002727.

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

Sequence in context: A119712 A273314 A281424 * A332081 A213557 A273386

Adjacent sequences: A005742 A005743 A005744 * A005746 A005747 A005748

Keyword

easy,nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from Vladeta Jovovic, May 26 2000

Status

approved