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Search: id:A150087
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| A150087 |
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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, 1, 1), (0, 0, -1), (0, 0, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 6, 19, 66, 243, 929, 3676, 14808, 60805, 252986, 1065589, 4536809, 19477581, 84303710, 367160122, 1608825471, 7085704233, 31353847815, 139335954645, 621512821655, 2782177030111, 12492835133199, 56262640514675, 254057915721103, 1150053975016142, 5218025470526626, 23725098445219734
(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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150085 A005654 A150086 this_sequence A150088 A150089 A150090
Adjacent sequences: A150084 A150085 A150086 this_sequence A150088 A150089 A150090
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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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