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%I M1197 N0462
%S 1,1,1,2,4,9,26,101,950,376467
%N Number of nonisomorphic simple matroids (or geometries) with n points.
%C Counts simple matroids, which necessarily cannot have loops or parallel elements. Bansal (2012) shows that log log a(n) <= n - (3/2)log n + 2 log log n+O(1), which matches Knuth's lower bound up to second order terms. [Jonathan Vos Post, Jun 27 2012]
%D J. E. Blackburn, H. H. Crapo, and D. A. Higgs, A catalogue of combinatorial geometries, Math. Comp., 27 (1973), 155-166.
%D Crapo, Henry H.; Rota, Gian-Carlo; On the foundations of combinatorial theory. II. Combinatorial geometries. Studies in Appl. Math. 49 1970 109-133.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H N. Bansal and R. Pendavingh, <a href="http://arxiv.org/abs/1206.6270">On the number of matroids</a>, arXiv:1206.6270v1 [math.CO], Jun 27 2012.
%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="http://www.stp.dias.ie/~dukes/phd.html">Counting and Probability in Matroid Theory</a>, Ph.D. Thesis, Trinity College, Dublin, 2000.
%H Gordon Royle and Dillon Mayhew, <a href="http://people.csse.uwa.edu.au/gordon/matroid-integer-sequences.html">9-element matroids</a>
%H N. J. A. Sloane, <a href="/A002773/a002773.gif">Initial terms (* denotes 5 points in general position in 4-space)</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Matroid.html">Matroid.</a>
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%Y Cf. A055545, A056642. Row sums of A058730.
%K nonn,nice
%O 0,4
%A _N. J. A. Sloane_.
%E a(9) from Gordon Royle, Dec 23 2006
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