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Search: id:A150921
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| A150921 |
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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, 0), (-1, 0, 0), (0, 0, -1), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 9, 33, 145, 620, 2767, 12458, 56879, 261838, 1216407, 5678117, 26682723, 125847796, 596177017, 2833553145, 13508052345, 64572800642, 309401003271, 1485722170179, 7148272797563, 34452552963828, 166322187950381, 804104736390432, 3892832802399421, 18869556315728514, 91571013610329289
(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, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A122097 A073400 A048498 this_sequence A150922 A150923 A150924
Adjacent sequences: A150918 A150919 A150920 this_sequence A150922 A150923 A150924
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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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