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A053534 Triangle T(n,k) giving number of pairwise non-isomorphic (i.e., unlabeled) matroids of rank k on n points (n >= 0, 0<=k<=n). 5
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 7, 4, 1, 1, 5, 13, 13, 5, 1, 1, 6, 23, 38, 23, 6, 1, 1, 7, 37, 108, 108, 37, 7, 1, 1, 8, 58, 325, 940, 325, 58, 8, 1, 1, 9, 87, 1275, 190214, 190214, 1275, 87, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

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, On the number of matroids on a finite set, arXiv:math/0411557 [math.CO], 2004.

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements, arXiv:math/0702316 [math.CO], 2007 (see p. 7).

Index entries for sequences related to matroids

EXAMPLE

The triangle, transposed, begins:

k...n=0...n=1...n=2...n=3...n=4...n=5...n=6...n=7...n=8...n=9...

0.|.1.....1.....1.....1.....1.....1.....1.....1.....1.......1.....

1.|.......1.....2.....3.....4.....5.....6.....7.....8.......9.....

2.|.............1.....3.....7....13....23....37....58......87.....

3.|...................1.....4....13....38...108...325....1275.....

4.|.........................1.....5....23...108...940..190214.....

5.|...............................1.....6....37...325..190214.....

6.|.....................................1.....7....58....1275.....

7.|...........................................1.....8......87.....

8.|.................................................1.......9.....

9.|.........................................................1.....

Sum.1.....2.....4.....8....17....38....98...306..1724..383172

CROSSREFS

Row sums give A055545. Diagonals give A058682, A058693. Cf. A058669.

Sequence in context: A088699 A101515 A028657 * A104881 A171699 A104878

Adjacent sequences:  A053531 A053532 A053533 * A053535 A053536 A053537

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Dec 30 2000

EXTENSIONS

More terms from Jonathan Vos Post, Feb 14 2007

Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar and Max Alekseyev

STATUS

approved

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Last modified December 10 05:49 EST 2018. Contains 318044 sequences. (Running on oeis4.)