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A151163
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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, -1), (-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
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1, 3, 12, 47, 204, 878, 3968, 17803, 82220, 377922, 1770124, 8263106, 39081068, 184404572, 878441218, 4177688311, 20011075710, 95741595824, 460610249666, 2214191750810, 10690345538210, 51585548294942, 249795741928906, 1209158919457606, 5869758137491138, 28487789961960806, 138585842592865512
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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
| Sequence in context: A122450 A179648 A100389 * A151164 A151165 A151166
Adjacent sequences: A151160 A151161 A151162 * A151164 A151165 A151166
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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