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Search: id:A149214
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| A149214 |
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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, 0, -1), (-1, 0, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 4, 10, 42, 135, 587, 2117, 9440, 36222, 164694, 656791, 3031172, 12413214, 57948607, 241968630, 1139741739, 4830463288, 22915599452, 98276507899, 468915380663, 2030520732519, 9734368014373, 42492739197948, 204517567273130, 898863173003696, 4340712959643123, 19189286075324474
(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, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + 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: A007173 A114918 A149213 this_sequence A149215 A149216 A149217
Adjacent sequences: A149211 A149212 A149213 this_sequence A149215 A149216 A149217
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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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