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A053534
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Triangle T(n,k) giving number of nonisomorphic matroids of rank k on n labeled points (n >= 0, 0<=k<=n).
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3
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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; internal format)
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OFFSET
| 0,5
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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
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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
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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
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2000
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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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