The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058715 Number of loopless matroids of rank 3 on n labeled points. 2
1, 11, 106, 1232, 22172, 803583, 70820187, 16122092568 (list; graph; refs; listen; history; text; internal format)



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


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


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


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

Cf. A008277, A056442, A058720.

Sequence in context: A250416 A116011 A229070 * A140617 A224717 A163413

Adjacent sequences:  A058712 A058713 A058714 * A058716 A058717 A058718




N. J. A. Sloane, Dec 31 2000


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 09:22 EDT 2021. Contains 345358 sequences. (Running on oeis4.)