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 A058717 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 1, 1<=k<=n). 1
 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 9, 4, 1, 1, 8, 19, 16, 5, 1, 1, 10, 33, 44, 25, 6, 1, 1, 12, 51, 96, 85, 36, 7, 1, 1, 14, 73, 180, 225, 146, 49, 8, 1, 1, 16, 99, 304, 501, 456, 231, 64, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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. W. M. B. Dukes, On the number of matroids on a finite set EXAMPLE 1; 0,1; 0,1,1; 0,1,2,1; 0,1,4,3,1; ... MATHEMATICA t[n_, k_] := Sum[(-1)^(i-k)*Binomial[n, i]*Sum[Binomial[k, 2*j]*Binomial[i-k, 2*j], {j, 0, i-k}] , {i, 0, n}]; Table[t[n, k], {n, 0, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 21 2013 *) CROSSREFS Cf. A058716 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719. Sequence in context: A161492 A177976 A034781 * A110470 A055080 A034367 Adjacent sequences:  A058714 A058715 A058716 * A058718 A058719 A058720 KEYWORD nonn,tabl,nice AUTHOR N. J. A. Sloane, Dec 31 2000 EXTENSIONS Corrected and extended by Jean-François Alcover, Oct 21 2013 STATUS approved

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Last modified February 20 19:02 EST 2020. Contains 332082 sequences. (Running on oeis4.)