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A148139
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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, -1, 1), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}
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0
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1, 1, 2, 4, 11, 28, 95, 281, 1023, 3303, 12548, 42915, 169376, 603821, 2451317, 9026835, 37375225, 141235599, 593917404, 2291130138, 9761555193, 38299976245, 164959896704, 656575126112, 2853288824481, 11497050189301, 50344157260794, 205014587541319, 903691117379319, 3714144604397194
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148137 A148138 A005503 * A061860 A093960 A118311
Adjacent sequences: A148136 A148137 A148138 * A148140 A148141 A148142
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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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