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Search: id:A150227
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| A150227 |
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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, 1), (0, 1, -1), (0, 1, 1), (1, 0, 1)} |
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+0
1
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| 1, 2, 6, 21, 87, 320, 1378, 5734, 24390, 104847, 468509, 2014677, 9086639, 40512331, 181514161, 817438205, 3739814457, 16804267343, 77203662737, 352969349528, 1615132230644, 7418825839826, 34348050827280, 157446234193077, 730722286101755, 3383822047970392, 15662986091827772, 72724675112435270
(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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + 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, 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: A121726 A090805 A150226 this_sequence A033540 A147719 A115089
Adjacent sequences: A150224 A150225 A150226 this_sequence A150228 A150229 A150230
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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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