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Search: id:A150818
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| A150818 |
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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, 0, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 8, 31, 136, 603, 2762, 12762, 59796, 282112, 1340577, 6401082, 30701136, 147752628, 713229089, 3451491228, 16739404303, 81337802668, 395887118980, 1929701874676, 9418489826558, 46024023964585, 225139138344005, 1102394618779217, 5402637900253288, 26498720939616348, 130066658818109547
(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, 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
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Sequence in context: A150815 A150816 A150817 this_sequence A009567 A150819 A003175
Adjacent sequences: A150815 A150816 A150817 this_sequence A150819 A150820 A150821
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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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