%I #21 Sep 13 2023 23:18:35
%S 1,2,5,16,68,406,3807,75164,10607540
%N Number of matroids on n labeled points.
%C From _Lorenzo Sauras Altuzarra_, Aug 10 2023: (Start)
%C a(n) <= A014466(n).
%C a(n) <= A306020(n). (End)
%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. B. Dukes, <a href="https://arxiv.org/abs/math/0411557">The number of matroids on a finite set</a>, arXiv:math/0411557 [math.CO], 2004.
%H W. M. B. Dukes, <a href="http://emis.impa.br/EMIS/journals/SLC/wpapers/s51dukes.html">On the number of matroids on a finite set</a>, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g.
%H S. C. Locke, <a href="http://euler.math.fau.edu/locke/SmallMatroids.htm">Matroids</a>
%H <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%e The 16 possible sets E such that ({1, 2, 3}, E) is a matroid:
%e {{}}
%e {{}, {1}}
%e {{}, {2}}
%e {{}, {3}}
%e {{}, {1}, {2}}
%e {{}, {1}, {3}}
%e {{}, {2}, {3}}
%e {{}, {1}, {2}, {3}}
%e {{}, {1}, {2}, {1, 2}}
%e {{}, {1}, {3}, {1, 3}}
%e {{}, {2}, {3}, {2, 3}}
%e {{}, {1}, {2}, {3}, {1, 2}, {1, 3}}
%e {{}, {1}, {2}, {3}, {1, 2}, {2, 3}}
%e {{}, {1}, {2}, {3}, {1, 3}, {2, 3}}
%e {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}}
%e {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
%Y Row sums of A058669. Closely related to A114491.
%Y Cf. A014466 (abstract simplicial complexes), A055545 (unlabeled matroids), A306020.
%K nonn,nice,more
%O 0,2
%A _N. J. A. Sloane_, Dec 30 2000