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Search: id:A150886
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| A150886 |
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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, 0, 1), (0, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 2, 8, 33, 150, 697, 3304, 15856, 76779, 373987, 1830987, 8995672, 44323228, 218889525, 1082922623, 5365602826, 26617684027, 132178009958, 656929238725, 3267295325023, 16260065946198, 80962304089982, 403308862138424, 2009838430795841, 10019154307564865, 49960740258061616, 249194818499378273
(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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150883 A150884 A150885 this_sequence A150887 A150888 A030977
Adjacent sequences: A150883 A150884 A150885 this_sequence A150887 A150888 A150889
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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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