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Search: id:A148415
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| A148415 |
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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, 1, -1), (1, -1, 1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 5, 17, 61, 229, 905, 3637, 15030, 63386, 272276, 1187268, 5239511, 23349563, 104935694, 475085078, 2165031594, 9924717432, 45736336780, 211759771698, 984569348155, 4594952651327, 21517502203089, 101076573807352, 476152633322594, 2248955765507576, 10647947497907067, 50526530559511271
(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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + 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
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Sequence in context: A150010 A150011 A112832 this_sequence A148416 A003456 A109084
Adjacent sequences: A148412 A148413 A148414 this_sequence A148416 A148417 A148418
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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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