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A057524
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Number of 3 x n binary matrices without unit columns up to row and column permutations.
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15
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1, 3, 7, 14, 25, 41, 64, 95, 136, 189, 256, 339, 441, 564, 711, 885, 1089, 1326, 1600, 1914, 2272, 2678, 3136, 3650, 4225, 4865, 5575, 6360, 7225, 8175, 9216, 10353, 11592, 12939, 14400, 15981, 17689, 19530, 21511, 23639, 25921, 28364, 30976
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Unit column of a binary matrix is a column with only one 1. First differences of a(n) give number of minimal 3-covers of an unlabeled n-set that cover 3 points of that set uniquely (if offset is 3).
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LINKS
| Author?, Table of n, a(n) for n = 0..1374
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FORMULA
| (1/6)*(Z(S_n; 5, 5, ...)+3*Z(S_n; 3, 5, 3, 5, ...)+2*Z(S_n; 2, 2, 5, 2, 2, 5, ...)) where Z(S_n; x_1, x_2, x_3, ...) is cycle index of symmetric group S_n of degree n. G.f. : 1/(1-x^3)/(1-x^2)/(1-x)^3.
Let P(i,k) be the number of integer partitions of n into k parts, then with k=3 we have a(n) = sum_{m=1}^{n} sum_{i=k}^{m} P(i,k). - Thomas Wieder (thomas.wieder(AT)t-online.de), Feb 18 2007
a(n)=sum_{m=0}^{n} (n-m+1)*IntegerPart[((m+3)^2+3)/12] [From Renzo Benedetti (benedetti.renzo(AT)gmail.com), Sep 30 2009]
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EXAMPLE
| There are 7 binary 3x2 matrices without unit columns up to row and column permutations:
[0 0] [0 0] [0 0] [0 1] [0 1] [0 1] [1 1]
[0 0] [0 1] [1 1] [0 1] [1 0] [1 1] [1 1]
[0 0] [0 1] [1 1] [0 1] [1 1] [1 1] [1 1].
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CROSSREFS
| Cf. A038846 for labeled case.
Cf. A000217, A002623, A002620.
Sequence in context: A171973 A004006 A089240 * A011795 A051170 A193911
Adjacent sequences: A057521 A057522 A057523 * A057525 A057526 A057527
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 07 2000
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