OFFSET
1,3
COMMENTS
Alternatively, number of linear geometries on n (labeled) points. For the unlabeled case see A001200.
Also a(n) = 1 + number of simple rank-3 matroids on n (labeled) elements; a(n) = number of 2-partitions of a set of size n.
REFERENCES
L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.
J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 19 (1967), 421-437.
J. A. Thas, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 21 (1969), 57-66.
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. Dukes, Bounds on the number of generalized partitions and some applications, Australas. J. Combin. 28 (2003), 257-261.
W. M. B. Dukes, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.
CROSSREFS
KEYWORD
nice,more,nonn
AUTHOR
W. M. B. Dukes (dukes(AT)stp.dias.ie), Aug 28 2000
EXTENSIONS
a(9) and a(10) from Gordon Royle, May 29 2006
STATUS
approved