

A058715


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


2




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, SÃ©minaire 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: 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



