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A149172
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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), (-1, 0, -1), (-1, 0, 0), (0, -1, 1), (1, 1, 0)}
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0
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1, 1, 4, 10, 33, 117, 389, 1471, 5400, 20343, 79235, 305897, 1209618, 4815788, 19257434, 77913848, 316467071, 1292277438, 5311275382, 21899703829, 90691380350, 377154613794, 1572516268371, 6579906312561, 27608923900448, 116114796021967, 489683028608476, 2069286621698950, 8762544387852487
(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, k, -1 + n] + aux[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]]; 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: A007716 A122948 A149171 * A105680 A066454 A022445
Adjacent sequences: A149169 A149170 A149171 * A149173 A149174 A149175
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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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