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A053534 Triangle T(n,k) giving number of nonisomorphic matroids of rank k on n labeled points (n >= 0, 0<=k<=n). +0
4
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; listen)
OFFSET

0,5

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, On the number of matroids on a finite set

Dillon Mayhew and Gordon F. Royle, Matroids with nine elements (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 this_sequence A104881 A104878 A135597

Adjacent sequences: A053531 A053532 A053533 this_sequence A053535 A053536 A053537

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2000

EXTENSIONS

More terms from Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 14 2007

Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 03 2008 at the suggestion of R. J. Mathar and Max Alekseyev

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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