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A053534
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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).
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6
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n,0) = 1 for n >= 0.
T(n,1) = n for n >= 1.
T(n,2) = -n + Sum_{k = 1..n} p(k) for n >= 2, where p(k) = A000041(k). [Dukes (2004), Theorem 2.1.] (End)
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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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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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