A058716 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,9

LINKS

Table of n, a(n) for n=0..44.

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

EXAMPLE

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

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;

...

CROSSREFS

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

Sequence in context: A301422 A055340 A119328 * A048723 A364386 A088455

Adjacent sequences: A058713 A058714 A058715 * A058717 A058718 A058719

KEYWORD

nonn,tabl,nice,hard

AUTHOR

N. J. A. Sloane, Dec 31 2000

EXTENSIONS

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

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

STATUS

approved