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A151431
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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), (-1, 0), (0, 1), (1, -1), (1, 1)}.
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0
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1, 1, 3, 8, 28, 101, 382, 1494, 6006, 24743, 103721, 441326, 1901396, 8281588, 36410636, 161392093, 720535739, 3237425269, 14629265198, 66446525314, 303203629717, 1389390196669, 6391187172587, 29502997060589, 136632723710850, 634655970861437, 2956108318526311, 13804298972322323, 64616451021696646
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OFFSET
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0,3
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LINKS
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M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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MATHEMATICA
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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] + aux[1 + i, 1 + j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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