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A058720
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Triangle T(n,k) giving the number of simple matroids of rank k on n labeled points (n >= 2, 2 <= k <= n).
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7
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1, 1, 1, 1, 5, 1, 1, 31, 16, 1, 1, 352, 337, 42, 1, 1, 8389, 18700, 2570, 99, 1, 1, 433038, 7642631, 907647, 16865, 219, 1
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OFFSET
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2,5
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LINKS
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FORMULA
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T(n, n-1) = 2^n - 1 - binomial(n+1,2) = A002662(n) for n >= 2. [Dukes (2004), Lemma 2.2(i).]
T(n, n-2) = A100728(n) = A000110(n+1) + binomial(n+3,4) + 2*binomial(n+1,4) - 2^n - 2^(n-1)*binomial(n+1,2). [Dukes (2004), Lemma 2.2(iii).]
(End)
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EXAMPLE
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Triangle T(n,k) (with rows n >= 2 and columns k >= 2) begins as follows:
1;
1, 1;
1, 5, 1;
1, 31, 16, 1;
1, 352, 337, 42, 1;
1, 8389, 18700, 2570, 99, 1;
1, 433038, 7642631, 907647, 16865, 219, 1;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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