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A058716
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Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0<=k<=n).
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6
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1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 6, 9, 4, 1, 0, 1, 10, 25, 18, 5, 1, 0, 1, 14, 70, 85, 31, 6, 1, 0, 1, 21, 217, 832, 288, 51, 7, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| A signed version is given by A119328. - Paul Barry (pbarry(AT)wit.ie), May 14 2006
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LINKS
| W. M. B. Dukes, Tables of matroids
W. M. B. Dukes, Counting and Probability in Matroid Theory, Ph.D. Thesis, Trinity College, Dublin, 2000.
Index entries for sequences related to matroids
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FORMULA
| T(n,k)=sum{i=0..n, (-1)^(i-k)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}; Column k has g.f. (x/(1-x))^k*sum{j=0..k, C(k,2j)x^(2j)}. - Paul Barry (pbarry(AT)wit.ie), May 14 2006
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EXAMPLE
| 1; 0,1; 0,1,1; 0,1,2,1; 0,1,4,3,1; ...
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MATHEMATICA
| t[n_, k_] := Sum[ (-1)^(i - k)*Binomial[n, i]* Sum[ Binomial[k, 2j]*Binomial[i - k, 2j], {j, 0, i - k}], {i, 0, n}]; Flatten[ Table[ t[n, k], {n, 0, 10}, {k, 0, n}]] (* From Jean-François Alcover, Jan 20 2012, after Paul Barry *) - This code does not produce the sequence. Something is wrong. - T. D. Noe Jan 20 2012
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CROSSREFS
| Cf. A058717 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.
Sequence in context: A055277 A055340 A119328 * A048723 A088455 A004248
Adjacent sequences: A058713 A058714 A058715 * A058717 A058718 A058719
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2000
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