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Search: id:A149496
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| A149496 |
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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, -1, 0), (-1, 0, -1), (0, -1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 9, 45, 109, 497, 1505, 6133, 21789, 82533, 321777, 1194945, 4811085, 18219585, 73076577, 286306473, 1134972601, 4568099273, 18063724073, 73541366101, 293534062209, 1194924730629, 4838269689497, 19642019715565, 80442812392417, 326934305905229, 1345821122024457, 5501463899445453
(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[i, 1 + j, 1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A123822 A145031 A121724 this_sequence A149497 A149498 A149499
Adjacent sequences: A149493 A149494 A149495 this_sequence A149497 A149498 A149499
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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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