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A151381
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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, -1)}.
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0
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1, 1, 1, 2, 4, 8, 18, 41, 97, 236, 584, 1474, 3770, 9767, 25575, 67592, 180128, 483502, 1306308, 3549830, 9697162, 26615698, 73366980, 203034787, 563901485, 1571351150, 4392057592, 12310850747, 34597448119, 97466655175, 275202241799, 778693720420, 2207705622668, 6270783269882, 17842662379410
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OFFSET
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0,4
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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]]; 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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