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

 Hints (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)
 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 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, SÃ©minaire Lotharingien de Combinatoire 51 (2004), Article B51g. 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: A250416 A116011 A229070 * 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

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.

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