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Search: id:A149245
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| A149245 |
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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, -1), (-1, 0, 0), (-1, 0, 1), (0, -1, 1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 11, 36, 138, 470, 1811, 6957, 26509, 106308, 418838, 1680174, 6831180, 27657994, 113594502, 467388473, 1929858509, 8021111685, 33391836563, 139565619390, 585228693864, 2459366708678, 10363035574570, 43773488086081, 185231446531915, 785496551225606, 3337214105223772
(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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A149243 A112849 A149244 this_sequence A054105 A017939 A130494
Adjacent sequences: A149242 A149243 A149244 this_sequence A149246 A149247 A149248
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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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