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Search: id:A026670
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| A026670 |
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Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 1, T(n,1) = T(n,n-1) = n-1; for n >= 2, T(n,k) = T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if n is even and k = n/2, else T(n,k) = T(n-1,k-1)+T(n-1,k). |
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17
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| 1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 5, 11, 5, 1, 1, 6, 16, 16, 6, 1, 1, 7, 22, 43, 22, 7, 1, 1, 8, 29, 65, 65, 29, 8, 1, 1, 9, 37, 94, 173, 94, 37, 9, 1, 1, 10, 46, 131, 267, 267, 131, 46, 10, 1, 1, 11, 56, 177, 398, 707, 398, 177, 56, 11, 1, 1, 12, 67
(list; table; graph; listen)
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OFFSET
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1,5
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LINKS
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Rob Arthan, Comments on A026674, A026725, A026670
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FORMULA
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T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) for i=j.
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EXAMPLE
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E.g. 11 = T(4, 2) = T(3, 1) + T(2, 2) + T(3, 2) = 4 + 3 + 4.
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CROSSREFS
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Cf. A026674.
Sequence in context: A050177 A013580 A147290 this_sequence A131402 A026626 A136482
Adjacent sequences: A026667 A026668 A026669 this_sequence A026671 A026672 A026673
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Formula corrected by David Perkinson (davidp(AT)reed.edu), Sep 19 2001 and also by Rob Arthan, Jan 16 2003
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