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Search: id:A150758
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| A150758 |
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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), (0, 1, -1), (0, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 8, 29, 136, 569, 2745, 12313, 60047, 278785, 1370631, 6489242, 32063338, 153792544, 762138261, 3688921333, 18318089997, 89237992514, 443789885981, 2172310292634, 10814897638178, 53131649255585, 264732166502829, 1304291033304278, 6502789627778453, 32110558081119880, 160171847394826059
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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
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Sequence in context: A150755 A150756 A150757 this_sequence A009419 A000162 A052437
Adjacent sequences: A150755 A150756 A150757 this_sequence A150759 A150760 A150761
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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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