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A148131
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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, 0), (-1, 0, 1), (1, 0, 0), (1, 1, -1)}
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0
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1, 1, 2, 4, 11, 27, 88, 251, 865, 2647, 9625, 31124, 117187, 394565, 1521086, 5271938, 20758265, 73741969, 294723790, 1067134981, 4321252882, 15901492296, 65085037328, 242796852919, 1002700099800, 3784053269508, 15751175996564, 60050158574561, 251634551218974, 967830162075301, 4079842369899290
(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, 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: A086441 A148130 A131482 * A205504 A099412 A100094
Adjacent sequences: A148128 A148129 A148130 * A148132 A148133 A148134
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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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