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A151497
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 1), (0, -1), (1, 0)}
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0
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1, 0, 1, 1, 2, 5, 10, 21, 56, 126, 294, 792, 1914, 4719, 12870, 32461, 82940, 228514, 593164, 1553630, 4316572, 11438076, 30509934, 85359210, 229719538, 621361560, 1748563730, 4762954770, 13025860020, 36837179385, 101317593480, 279567203745, 793968265740, 2201121030510, 6118456219260, 17440129166730
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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LINKS
| M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
| aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A052540 A018106 A192317 * A110744 A079342 A034456
Adjacent sequences: A151494 A151495 A151496 * A151498 A151499 A151500
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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