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A151057
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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, -1, 0), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.
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0
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1, 3, 10, 37, 147, 609, 2589, 11247, 49728, 222781, 1008483, 4606395, 21201393, 98198734, 457304438, 2139893842, 10055475710, 47425035188, 224408115290, 1065007959055, 5067771681127, 24172350026588, 115549216225597, 553450943733997, 2655709904673914, 12764620743315571, 61447692280275054
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OFFSET
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0,2
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LINKS
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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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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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KEYWORD
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nonn,walk,changed
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AUTHOR
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STATUS
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approved
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