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%I #19 Nov 14 2023 09:22:21
%S 1,1,2,6,32,353,8390,433039,50166354,13480967630
%N Number of linear spaces on n (labeled) points.
%C Alternatively, number of linear geometries on n (labeled) points. For the unlabeled case see A001200.
%C 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.
%D L. M. Batten and A. Beutelspacher: The theory of finite linear spaces, Cambridge Univ. Press, 1993 (see the Appendix).
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 303, #42.
%D J. Doyen, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 19 (1967), 421-437.
%D J. A. Thas, Sur le nombre d'espaces linéaires non isomorphes de n points, Bull. Soc. Math. Belg. 21 (1969), 57-66.
%H W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H W. M. B. Dukes, <a href="https://web.archive.org/web/20030208144026/http://www.stp.dias.ie/~dukes/phd.html">Counting and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, Dublin, 2000.
%H W. M. Dukes, <a href="http://ajc.maths.uq.edu.au/pdf/28/ajc_v28_p257.pdf">Bounds on the number of generalized partitions and some applications</a>, Australas. J. Combin. 28 (2003), 257-261.
%H W. M. B. Dukes, <a href="http://arXiv.org/abs/math.CO/0411557">On the number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%Y Corrected version of A001199. Cf. A002773, A001200, A031436, A058731.
%K nice,more,nonn
%O 1,3
%A W. M. B. Dukes (dukes(AT)stp.dias.ie), Aug 28 2000
%E a(9) and a(10) from _Gordon Royle_, May 29 2006
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