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Search: id:A148328
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| A148328 |
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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, 0, 1), (1, -1, 0), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 5, 14, 42, 130, 415, 1365, 4592, 15727, 54593, 191610, 679420, 2430721, 8763775, 31807636, 116106836, 426029867, 1570602958, 5814799002, 21610381589, 80590043893, 301484592756, 1131111868525, 4255026611884, 16045919249512, 60646837901675, 229700320188818, 871691280039250, 3314013545656012
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, 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
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Sequence in context: A148326 A148327 A092493 this_sequence A080937 A054392 A006930
Adjacent sequences: A148325 A148326 A148327 this_sequence A148329 A148330 A148331
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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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