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A058715
Number of loopless matroids of rank 3 on n labeled points.
2
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
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.
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).
Sequence in context: A116011 A229070 A365775 * A140617 A224717 A163413
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