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A151267
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (1, -1), (1, 1)}
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0
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1, 1, 3, 7, 21, 55, 165, 457, 1371, 3909, 11727, 33993, 101979, 298629, 895887, 2640931, 7922793, 23460851, 70382553, 209078319, 627234957, 1867531435, 5602594305, 16709292259, 50127876777, 149690954499, 449072863497, 1342297451651, 4026892354953, 12045410486339, 36136231459017, 108154061971965
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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.
A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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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[1 + i, -1 + j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 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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