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A026736
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Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, 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)/2, else T(n,k)=T(n-1,k-1)+T(n-1,k).
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30
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 6, 4, 1, 1, 6, 11, 10, 5, 1, 1, 7, 22, 21, 15, 6, 1, 1, 8, 29, 43, 36, 21, 7, 1, 1, 9, 37, 94, 79, 57, 28, 8, 1, 1, 10, 46, 131, 173, 136, 85, 36, 9, 1, 1, 11, 56, 177, 398, 309, 221, 121, 45, 10, 1, 1, 12, 67, 233, 575
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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FORMULA
| T(n, k) = number of paths from (0, 0) to (n-k, k) in 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, i+2)-to-(i+1, i+3) for i >= 0.
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EXAMPLE
| 1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 5, 6, 4, 1;
1, 6, 11, 10, 5, 1;
1, 7, 22, 21, 15, 6, 1;
1, 8, 29, 43, 36, 21, 7, 1;
1, 9, 37, 94, 79, 57, 28, 8, 1;
1, 10, 46, 131, 173, 136, 85, 36, 9, 1;
1, 11, 56, 177, 398, 309, 221, 121, 45, 10, 1;
1, 12, 67, 233, 575
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CROSSREFS
| Sequence in context: A053538 A138201 A154221 * A050446 A144048 A113983
Adjacent sequences: A026733 A026734 A026735 * A026737 A026738 A026739
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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