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A133687
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Triangle with number of equivalence classes of n X n matrices over {0,1} with rows and columns summing to k (0<=k<=n), where equivalence is defined by row and column permutations.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 4, 7, 4, 1, 1, 1, 1, 4, 16, 16, 4, 1, 1, 1, 1, 7, 51, 194, 51, 7, 1, 1, 1, 1, 8, 224, 3529, 3529, 224, 8, 1, 1, 1, 1, 12, 1165, 121790, 601055, 121790, 1165, 12, 1, 1, 1, 1, 14, 7454, 5582612, 156473848, 5582612, 7454, 14, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| a(n,k) = a(n,n-k); when 0 and 1 are switched, the number of equivalence classes remain the same.
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FORMULA
| a(n,2) = A002865(n); a(n,3) = A000512(n); a(n,4) = A000513(n); a(n,5) = A000516(n); Sum(a(n, k), n, k>=1) = A000519;
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EXAMPLE
| Triangle begins:
1
1, 1
1, 1, 1
1, 1, 1, 1
1, 1, 2, 1, 1
1, 1, 2, 2, 1, 1
1, 1, 4, 7, 4, 1, 1
1, 1, 4, 16, 16, 4, 1, 1
1, 1, 7, 51, 194, 51, 7, 1, 1
1, 1, 8, 224, 3529, 3529, 224, 8, 1, 1
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CROSSREFS
| Sequence in context: A047996 A063686 A008327 * A097587 A001179 A001876
Adjacent sequences: A133684 A133685 A133686 * A133688 A133689 A133690
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KEYWORD
| nonn,tabl
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AUTHOR
| Joost Vermeij (joost_vermeij(AT)live.nl), Jan 04 2008
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