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Search: id:A150890
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| A150890 |
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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, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 2, 8, 34, 152, 698, 3270, 15530, 74495, 359929, 1748735, 8533798, 41791676, 205246149, 1010356859, 4983305505, 24618899401, 121792258481, 603229234767, 2990780107566, 14841112221648, 73701912887981, 366251823036920, 1821102270776343, 9059671077037949, 45090854393925053, 224512441552195896
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A026387 A085362 A150889 this_sequence A150891 A074606 A002928
Adjacent sequences: A150887 A150888 A150889 this_sequence A150891 A150892 A150893
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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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