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A058673 Number of matroids on n labeled points.

%I A058673 #21 Sep 13 2023 23:18:35
%S A058673 1,2,5,16,68,406,3807,75164,10607540
%N A058673 Number of matroids on n labeled points.
%C A058673 From _Lorenzo Sauras Altuzarra_, Aug 10 2023: (Start)
%C A058673 a(n) <= A014466(n).
%C A058673 a(n) <= A306020(n). (End)
%H A058673 W. M. B. Dukes, <a href="http://www.stp.dias.ie/~dukes/matroid.html">Tables of matroids</a>.
%H A058673 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 A058673 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 A058673 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 A058673 S. C. Locke, <a href="http://euler.math.fau.edu/locke/SmallMatroids.htm">Matroids</a>
%H A058673 <a href="/index/Mat#matroid">Index entries for sequences related to matroids</a>
%e A058673 The 16 possible sets E such that ({1, 2, 3}, E) is a matroid:
%e A058673   {{}}
%e A058673   {{}, {1}}
%e A058673   {{}, {2}}
%e A058673   {{}, {3}}
%e A058673   {{}, {1}, {2}}
%e A058673   {{}, {1}, {3}}
%e A058673   {{}, {2}, {3}}
%e A058673   {{}, {1}, {2}, {3}}
%e A058673   {{}, {1}, {2}, {1, 2}}
%e A058673   {{}, {1}, {3}, {1, 3}}
%e A058673   {{}, {2}, {3}, {2, 3}}
%e A058673   {{}, {1}, {2}, {3}, {1, 2}, {1, 3}}
%e A058673   {{}, {1}, {2}, {3}, {1, 2}, {2, 3}}
%e A058673   {{}, {1}, {2}, {3}, {1, 3}, {2, 3}}
%e A058673   {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}}
%e A058673   {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
%Y A058673 Row sums of A058669. Closely related to A114491.
%Y A058673 Cf. A014466 (abstract simplicial complexes), A055545 (unlabeled matroids), A306020.
%K A058673 nonn,nice,more
%O A058673 0,2
%A A058673 _N. J. A. Sloane_, Dec 30 2000