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Search: id:A149849
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| A149849 |
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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, 1, -1), (0, 1, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 14, 46, 144, 540, 1952, 7066, 27326, 104192, 402370, 1583626, 6253532, 24935669, 99650433, 402653095, 1634611082, 6627794165, 27175594747, 111655473179, 458521078228, 1898047857400, 7871222083602, 32657227815791, 136120126645941, 568766898128386, 2378607344430242, 9970920272017160
(list; graph; listen)
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OFFSET
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0,2
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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, j, 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, 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: A101536 A149847 A149848 this_sequence A149850 A149851 A149852
Adjacent sequences: A149846 A149847 A149848 this_sequence A149850 A149851 A149852
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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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