A058715 Number of loopless matroids of rank 3 on n labeled points.

1, 11, 106, 1232, 22172, 803583, 70820187, 16122092568

Offset

3,2

Comments

The sequence was updated based on more recent references by W. M. B. Dukes. The calculation of a(9) and a(10) depends on the values of A056642 for n = 9 and n = 10. Note that (A056642) - 1 is column k = 3 of A058720. - Petros Hadjicostas, Oct 09 2019

Links

Table of n, a(n) for n=3..10.

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

Formula

a(n) = Sum_{i = 3..n} Stirling2(n,i) * (A056642(i) - 1) = Sum_{i = 3..n} A008277(n,i) * A058720(n,3) for n >= 3. [Dukes (2004), p. 3; see the equation with the Stirling numbers of the second kind.] - Petros Hadjicostas, Oct 10 2019

Crossrefs

Column k=3 of both A058710 and A058711 (which are the same except for column k=0).

Cf. A008277, A056442, A058720.

Sequence in context: A116011 A229070 A365775 * A140617 A224717 A163413

Adjacent sequences: A058712 A058713 A058714 * A058716 A058717 A058718

Keyword

nonn

Author

N. J. A. Sloane, Dec 31 2000

Extensions

a(8) corrected by and more terms from Petros Hadjicostas, Oct 09 2019

Status

approved