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A149663
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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, -1, 1), (0, 0, -1), (0, 1, -1), (1, 1, 1)}
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0
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1, 1, 5, 17, 61, 241, 1013, 4073, 17069, 73505, 316133, 1361337, 5980189, 26406801, 116548949, 518274729, 2322720077, 10418420609, 46852187525, 211863806873, 960661273085, 4360754376177, 19857020638645, 90694294866057, 414765463767725, 1899929428731233, 8724174474617573, 40124073832013433
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, 1 + j, -1 + 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
| Sequence in context: A192146 A007483 A149662 * A149664 A149665 A149666
Adjacent sequences: A149660 A149661 A149662 * A149664 A149665 A149666
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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