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Search: id:A150273
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| A150273 |
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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, -1), (-1, -1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)} |
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+0
1
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| 1, 2, 6, 22, 92, 364, 1598, 6824, 30404, 136764, 617446, 2831276, 13031622, 60346428, 281845432, 1316928654, 6197429960, 29231903134, 138286736940, 656927696126, 3123870663170, 14906011474554, 71252038551888, 341159241443052, 1637518071666842, 7866975262786576, 37870754508194960, 182537355530341254
(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[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A124293 A107591 A155866 this_sequence A001181 A130579 A107945
Adjacent sequences: A150270 A150271 A150272 this_sequence A150274 A150275 A150276
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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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