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A148803
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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, 0, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1)}
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0
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1, 1, 3, 8, 26, 83, 281, 971, 3417, 12264, 44438, 162904, 602266, 2241764, 8400548, 31634918, 119702435, 454780012, 1733848968, 6631814922, 25436402695, 97810174385, 376967520192, 1455826275320, 5632909116247, 21831857984083, 84746834213967, 329439820828496, 1282316672529298, 4997344941893617
(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, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A205775 A148802 A194690 * A148804 A148805 A000237
Adjacent sequences: A148800 A148801 A148802 * A148804 A148805 A148806
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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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