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A057970 5 x n binary matrices with 1 unit column up to row and column permutations. 3
1, 8, 54, 333, 1896, 9874, 47164, 207112, 840323, 3168506, 11170331, 37034409, 116095018, 345785753, 982835676, 2676217504, 7005306389, 17681946594, 43153532167, 102080966243, 234565062960, 524594120393, 1143910860870 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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 6 points of that set uniquely (if offset is 6).
LINKS
FORMULA
Number of 5 x n binary matrices with k unit columns up to row and column permutations is coefficient of x^k in (1/5!)*(Z(S_n; 27 + 5*x, 27 + 5*x^2, ...) + 10*Z(S_n; 13 + 3*x, 27 + 5*x^2, 13 + 3*x^3, 27 + 5*x^4, ...) + 15*Z(S_n; 7 + x, 27 + 5*x^2, 7 + x^3, 27 + 5*x^4, ...) + 20*Z(S_n; 6 + 2*x, 6 + 2*x^2, 27 + 5*x^3, 6 + 2*x^4, 6 + 2*x^5, 27 + 5*x^6, ...) + 20*Z(S_n; 4, 6 + 2*x^2, 13 + 3*x^3, 6 + 2*x^4, 4, 27 + 5*x^6, 4, 6 + 2*x^8, 13 + 3*x^9, 6 + 2*x^10, 4, 27 + 5*x^12, ...) + 30*Z(S_n; 3 + x, 7 + x^2, 3 + x^3, 27 + 5*x^4, 3 + x^5, 7 + x^6, 3 + x^7, 27 + 5*x^8, ...) + 24*Z(S_n; 2, 2, 2, 2, 27 + 5*x^5, 2, 2, 2, 2, 27 + 5*x^10, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n.
G.f.: x/120*(5/(1 - x^1)^27 + 30/(1 - x^1)^13/(1 - x^2)^7 + 15/(1 - x^1)^7/(1 - x^2)^10 + 40/(1 - x^1)^6/(1 - x^3)^7 + 30/(1 - x^1)^3/(1 - x^2)^2/(1 - x^4)^5).
CROSSREFS
Sequence in context: A037966 A091433 A081899 * A208310 A154235 A289796
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Oct 21 2000
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)