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Search: id:A149034
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| A149034 |
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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, -1, 0), (1, 0, 1)} |
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+0
1
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| 1, 1, 3, 10, 34, 129, 502, 2032, 8462, 35852, 154565, 675899, 2987199, 13340857, 60068598, 272467777, 1243944728, 5710995281, 26354122717, 122157252775, 568553772397, 2655883548577, 12447898038513, 58520081537723, 275877728447581, 1303890813173164, 6177081403785151, 29327215806292682
(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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A047032 A149032 A149033 this_sequence A149035 A099907 A128735
Adjacent sequences: A149031 A149032 A149033 this_sequence A149035 A149036 A149037
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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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