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A058716 Triangle T(n,k) giving number of nonisomorphic loopless matroids of rank k on n labeled points (n >= 0, 0 <= k <= n). 5
1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 6, 9, 4, 1, 0, 1, 10, 25, 18, 5, 1, 0, 1, 14, 70, 85, 31, 6, 1, 0, 1, 21, 217, 832, 288, 51, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
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.
EXAMPLE
Triangle T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows:
1;
0, 1;
0, 1, 1;
0, 1, 2, 1;
0, 1, 4, 3, 1;
0, 1, 6, 9, 4, 1;
0, 1, 10, 25, 18, 5, 1;
0, 1, 14, 70, 85, 31, 6, 1;
0, 1, 21, 217, 832, 288, 51, 7, 1;
...
CROSSREFS
Cf. A058717 (same except for border), A058710, A058711. Row sums give A058718. Diagonals give A000065, A058719.
Sequence in context: A301422 A055340 A119328 * A048723 A364386 A088455
KEYWORD
nonn,tabl,nice,hard
AUTHOR
N. J. A. Sloane, Dec 31 2000
EXTENSIONS
Corrected and extended by Jean-François Alcover, Oct 21 2013
Reverted to original data by Sean A. Irvine, Aug 16 2022
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)