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Search: id:A150934
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| A150934 |
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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), (1, 0, -1), (1, 0, 1), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 33, 155, 652, 3113, 13874, 66837, 307272, 1488777, 6975715, 33934993, 161025010, 785710159, 3761589709, 18397686843, 88656750924, 434438606787, 2103945744667, 10326023778843, 50202224491800, 246715654083731, 1203177588869660, 5919654714954755, 28941493241781162, 142533052461358635
(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[-1 + 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: A150931 A150932 A150933 this_sequence A150935 A150936 A109719
Adjacent sequences: A150931 A150932 A150933 this_sequence A150935 A150936 A150937
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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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