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Search: id:A150024
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| A150024 |
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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, 1, 1), (1, -1, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 5, 18, 67, 265, 1099, 4615, 19918, 86872, 384831, 1723134, 7782492, 35456485, 162474523, 749303875, 3471551664, 16159342707, 75510910742, 354110285481, 1666053933555, 7860810672910, 37190149979929, 176363094591082, 838240103613605, 3992076916379348, 19048084412644487, 91045079127716986
(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[-1 + i, 1 + j, -1 + 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]]; 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: A150021 A150022 A150023 this_sequence A150025 A118814 A014271
Adjacent sequences: A150021 A150022 A150023 this_sequence A150025 A150026 A150027
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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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