A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0 <= k <= n).

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

Offset: 0

Author

N. J. A. Sloane, Dec 31 2000

Keywords

• nonn
• tabl
• nice
• hard

Examples

			Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:
  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;
  ...
		

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, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
• W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
• Index entries for sequences related to matroids

Crossrefs

Cf. A058717 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.

Extensions

Corrected and extended by Jean-François Alcover, Oct 21 2013

Reverted to original data by Sean A. Irvine, Aug 16 2022