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Search: id:A148389
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| A148389 |
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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, 0, 0), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 5, 16, 51, 175, 603, 2179, 7966, 30115, 115175, 447599, 1754566, 6960211, 27838776, 112401002, 457156790, 1872092533, 7709515518, 31925277406, 132858964434, 555535209096, 2332992606313, 9836786434533, 41626228814418, 176751460040269, 752917025247036, 3216949479854651
(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, 1 + k, -1 + n] + aux[-1 + i, j, 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: A121651 A054660 A148388 this_sequence A108529 A011819 A148390
Adjacent sequences: A148386 A148387 A148388 this_sequence A148390 A148391 A148392
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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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