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Search: id:A151159
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| A151159 |
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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), (0, 1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 3, 11, 47, 211, 967, 4545, 21595, 103560, 500728, 2432736, 11872654, 58147671, 285541655, 1405564858, 6931965131, 34241853082, 169380533106, 838827662629, 4158357094931, 20632504860970, 102449894560199, 509051595998291, 2530853483373135, 12589174896257329, 62650955770516782, 311914797202148112
(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, 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: A151157 A151158 A055731 this_sequence A151160 A151161 A124890
Adjacent sequences: A151156 A151157 A151158 this_sequence A151160 A151161 A151162
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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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