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 A058673 Number of matroids on n labeled points. 6
 1, 2, 5, 16, 68, 406, 3807, 75164, 10607540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Lorenzo Sauras Altuzarra, Aug 10 2023: (Start) a(n) <= A014466(n). a(n) <= A306020(n). (End) LINKS Table of n, a(n) for n=0..8. 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. B. Dukes, The number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004. W. M. B. Dukes, On the number of matroids on a finite set, Séminaire Lotharingien de Combinatoire 51 (2004), Article B51g. S. C. Locke, Matroids Index entries for sequences related to matroids EXAMPLE The 16 possible sets E such that ({1, 2, 3}, E) is a matroid: {{}} {{}, {1}} {{}, {2}} {{}, {3}} {{}, {1}, {2}} {{}, {1}, {3}} {{}, {2}, {3}} {{}, {1}, {2}, {3}} {{}, {1}, {2}, {1, 2}} {{}, {1}, {3}, {1, 3}} {{}, {2}, {3}, {2, 3}} {{}, {1}, {2}, {3}, {1, 2}, {1, 3}} {{}, {1}, {2}, {3}, {1, 2}, {2, 3}} {{}, {1}, {2}, {3}, {1, 3}, {2, 3}} {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}} {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} CROSSREFS Row sums of A058669. Closely related to A114491. Cf. A014466 (abstract simplicial complexes), A055545 (unlabeled matroids), A306020. Sequence in context: A002631 A107948 A220840 * A296675 A059295 A259408 Adjacent sequences: A058670 A058671 A058672 * A058674 A058675 A058676 KEYWORD nonn,nice,more AUTHOR N. J. A. Sloane, Dec 30 2000 STATUS approved

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Last modified March 1 15:55 EST 2024. Contains 370442 sequences. (Running on oeis4.)