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Search: id:A149516
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| A149516 |
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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, -1, -1), (1, -1, 1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 11, 49, 157, 629, 2319, 9309, 36067, 146735, 583717, 2403149, 9754979, 40462171, 166354683, 695612827, 2888616957, 12146055243, 50820925053, 214800425487, 904468489247, 3837974122189, 16240475548249, 69171748577847, 293963559264191, 1255748732370767, 5355420642656009
(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, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + 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: A142238 A149514 A149515 this_sequence A149517 A149518 A149519
Adjacent sequences: A149513 A149514 A149515 this_sequence A149517 A149518 A149519
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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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