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A057969 5 x n binary matrices without unit columns up to row and column permutations. 3
1, 5, 24, 115, 551, 2542, 11193, 46547, 182164, 670476, 2325506, 7624434, 23716419, 70253721, 198905506, 540079754, 1410786483, 3555443969, 8667153126, 20484365167, 47037898503, 105143200252, 229178029000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A unit column of a binary matrix is a column with only one 1. First differences of a(n) give number of minimal 5-covers of an unlabeled n-set that cover 5 points of that set uniquely (if offset is 5).

LINKS

Table of n, a(n) for n=0..22.

Vladeta Jovovic, The number of minimal covers of an unlabeled n-set that cover k points of that set uniquely

Vladeta Jovovic, Number of binary matrices with fixed number of unit columns up to row and column permutations

FORMULA

a(n)=(1/5!)*(Z(S_n; 27, 27, ...) + 10*Z(S_n; 13, 27, 13, 27, ...) + 15*Z(S_n; 7, 27, 7, 27, ...) + 20*Z(S_n; 6, 6, 27, 6, 6, 27, ...) + 20*Z(S_n; 4, 6, 13, 6, 4, 27, 4, 6, 13, 6, 4, 27, ...) + 30*Z(S_n; 3, 7, 3, 27, 3, 7, 3, 27, ...) + 24*Z(S_n; 2, 2, 2, 2, 27, 2, 2, 2, 2, 27, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n. G.f. : 1/120*(1/(1 - x^1)^27 + 10/(1 - x^1)^13/(1 - x^2)^7 + 15/(1 - x^1)^7/(1 - x^2)^10 + 20/(1 - x^1)^6/(1 - x^3)^7 + 20/(1 - x^1)^4/(1 - x^2)^1/(1 - x^3)^3/(1 - x^6)^2 + 30/(1 - x^1)^3/(1 - x^2)^2/(1 - x^4)^5 + 24/(1 - x^1)^2/(1 - x^5)^5).

CROSSREFS

Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963-A057968, A057970-A057972.

Sequence in context: A140766 A026388 A242509 * A004254 A086347 A200739

Adjacent sequences:  A057966 A057967 A057968 * A057970 A057971 A057972

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Oct 20 2000

STATUS

approved

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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)