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Search: id:A149658
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| A149658 |
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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, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 17, 59, 239, 995, 3967, 16685, 72029, 308013, 1326509, 5839973, 25751313, 113486965, 505253549, 2264923651, 10149497751, 45647471491, 206545814791, 936339133515, 4249377202291, 19357161132847, 88430112102083, 404359447342391, 1852486534010095, 8508801394789043, 39136469862569959
(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[-1 + i, j, 1 + 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: A105392 A090857 A149657 this_sequence A149659 A149660 A149661
Adjacent sequences: A149655 A149656 A149657 this_sequence A149659 A149660 A149661
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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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