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Search: id:A150218
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| A150218 |
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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), (0, 0, -1), (0, 1, 0), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 6, 21, 82, 321, 1299, 5392, 22871, 98108, 424699, 1856216, 8183556, 36317895, 161980553, 725942682, 3268471012, 14774712211, 67005494929, 304779943331, 1390265877349, 6358331776667, 29145901592320, 133874784240042, 616114068765967, 2840641129896737, 13118766404752789, 60677043758756303
(list; graph; listen)
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OFFSET
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0,2
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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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A150215 A150216 A150217 this_sequence A150219 A150220 A032347
Adjacent sequences: A150215 A150216 A150217 this_sequence A150219 A150220 A150221
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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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