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A151488
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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), (0, 1), (1, -1), (1, 0), (1, 1)}.
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0
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1, 1, 4, 13, 51, 207, 887, 3907, 17689, 81598, 382809, 1819544, 8748842, 42469534, 207900762, 1025103628, 5087012042, 25386558037, 127331796354, 641546957748, 3245566636974, 16479875939807, 83960810598237, 429073494547532, 2198921270348087, 11298292559488283, 58190917785493662, 300372279767201773
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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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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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