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A148334
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Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 1, 1), (0, 0, 1), (1, -1, 1), (1, 0, -1)}
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0
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1, 1, 2, 5, 14, 43, 147, 521, 1941, 7480, 29589, 119739, 493859, 2068429, 8783152, 37733105, 163756225, 717099427, 3165207986, 14069737107, 62939441266, 283160925349, 1280508190885, 5817930349391, 26546802485592, 121606719251131, 559072059863772, 2578817198577756, 11931845796002335
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..28.
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, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A137552 A137553 A149881 * A149882 A137554 A137555
Adjacent sequences: A148331 A148332 A148333 * A148335 A148336 A148337
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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