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A149027
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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, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}
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0
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1, 1, 3, 9, 39, 143, 645, 2603, 12089, 51843, 244625, 1085225, 5172639, 23504709, 112876019, 521562001, 2517993407, 11779732141, 57108894755, 269728321329, 1311947665271, 6242539439513, 30444460089423, 145731077374047, 712289602626021, 3426187222066247, 16777120269058485, 81025572922970219
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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
| Sequence in context: A059804 A065657 A149026 * A180741 A121101 A080635
Adjacent sequences: A149024 A149025 A149026 * A149028 A149029 A149030
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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