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Search: id:A148839
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| A148839 |
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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, 0, 1), (0, 0, -1), (0, 1, 1), (1, -1, 1)} |
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+0
1
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| 1, 1, 3, 8, 27, 90, 319, 1133, 4205, 15759, 60427, 233074, 913214, 3602736, 14365891, 57610031, 232900379, 946343007, 3869179663, 15888284571, 65568408186, 271629504874, 1129897836137, 4715762928864, 19749860841934, 82957158492855, 349484850458876, 1476158463333397, 6251072188077864
(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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A148836 A148837 A148838 this_sequence A148840 A047153 A000238
Adjacent sequences: A148836 A148837 A148838 this_sequence A148840 A148841 A148842
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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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