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Search: id:A148109
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| A148109 |
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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, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 4, 10, 28, 79, 240, 747, 2442, 8122, 27655, 95774, 338586, 1214670, 4409121, 16185295, 60075271, 225336394, 852030177, 3245779122, 12454403176, 48137170525, 187203702504, 731955128196, 2876702581314, 11364887602996, 45115533013767, 179849000456452, 719753549785382, 2891681302205292
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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
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Sequence in context: A123411 A128933 A106362 this_sequence A099216 A149819 A149820
Adjacent sequences: A148106 A148107 A148108 this_sequence A148110 A148111 A148112
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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