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Search: id:A148097
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| A148097 |
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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, 0, 1), (0, 0, 1), (0, 1, -1), (1, -1, 0)} |
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+0
1
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| 1, 1, 2, 4, 10, 26, 72, 210, 633, 1965, 6255, 20320, 67115, 225180, 765236, 2629300, 9128886, 31973878, 112868208, 401357573, 1436347656, 5170091107, 18710588629, 68041269378, 248527107385, 911543126026, 3355925436811, 12398020132566, 45952857513263, 170833589869361, 636858717536370, 2380437498466650
(list; graph; listen)
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OFFSET
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0,3
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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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A154835 A049145 A102407 this_sequence A148098 A049130 A101488
Adjacent sequences: A148094 A148095 A148096 this_sequence A148098 A148099 A148100
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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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