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A151506
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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, 1), (0, -1), (1, -1), (1, 0)}
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0
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1, 0, 1, 1, 5, 6, 33, 66, 262, 688, 2614, 7630, 28372, 91490, 333166, 1139686, 4172274, 14771196, 54529720, 198319758, 738538816, 2738271072, 10302251312, 38749276416, 147201935416, 560210700982, 2146843198772, 8250106899418, 31870249952754, 123485120302378, 480468887927340, 1874991897193156
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OFFSET
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0,5
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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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + 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
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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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