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A151406
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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, 0), (0, -1), (1, -1), (1, 1)}
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0
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1, 0, 1, 2, 4, 8, 31, 74, 180, 598, 1834, 4788, 14996, 49482, 143789, 435354, 1453804, 4561596, 13938918, 45872900, 150436644, 473005586, 1538113866, 5131580610, 16631971200, 54060256628, 180817311524, 599398780812, 1965766211768, 6566285301920, 22047832597671, 73217323048944, 244741654013110
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
| Sequence in context: A053364 A018355 A100083 * A053147 A128055 A061285
Adjacent sequences: A151403 A151404 A151405 * A151407 A151408 A151409
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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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