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A148160
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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, 1, 1), (0, 0, -1), (1, 0, 0)}
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0
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1, 1, 2, 4, 11, 31, 86, 246, 736, 2276, 7240, 22690, 72285, 234747, 771123, 2566400, 8493635, 28334539, 95604553, 324278488, 1108220193, 3778047729, 12939669749, 44644265673, 154504166115, 537300462031, 1866279782528, 6502091763142, 22768475794159, 79893282232247, 281289871201986, 989741714280930
(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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A193059 A034770 A002387 * A148161 A148162 A148163
Adjacent sequences: A148157 A148158 A148159 * A148161 A148162 A148163
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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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