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A151333
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Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 1), (0, 1), (1, -1)}.
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0
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1, 0, 2, 6, 42, 308, 2424, 21118, 194010, 1866896, 18674908, 192737280, 2042585592, 22142680360, 244772420336, 2752312897942, 31415853441050, 363394473652344, 4253708877703476, 50326069309616132, 601181906802967564, 7244698219481190376, 88003741534163878912, 1076851417694238454896
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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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, 2 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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