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Search: id:A150198
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| A150198 |
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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, 0), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 6, 21, 79, 309, 1253, 5199, 21953, 94078, 407603, 1782008, 7852152, 34826220, 155346976, 696396185, 3135324925, 14170200056, 64262626325, 292332241071, 1333529156881, 6098477626368, 27953506288502, 128399740959616, 590923668118531, 2724414394446939, 12581474056408749, 58190854507105448
(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[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: A026737 A111279 A150197 this_sequence A033321 A050203 A112806
Adjacent sequences: A150195 A150196 A150197 this_sequence A150199 A150200 A150201
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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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