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Search: id:A053534
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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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4
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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; listen)
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OFFSET
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0,5
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LINKS
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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
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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
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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
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KEYWORD
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nonn,tabl,nice,new
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AUTHOR
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njas, Dec 30 2000
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EXTENSIONS
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More terms from Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 14 2007
Edited by njas, Jul 03 2008 at the suggestion of R. J. Mathar and Max Alekseyev
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