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Search: id:A148878
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| A148878 |
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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, 0), (0, 1, -1), (0, 1, 1), (1, -1, 0)} |
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+0
1
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| 1, 1, 3, 8, 30, 95, 373, 1337, 5491, 20879, 87823, 348878, 1495592, 6116233, 26582687, 111153122, 488390316, 2076955693, 9206018343, 39681877464, 177159455338, 772030567083, 3467620937271, 15248904120655, 68844612742745, 305061781752215, 1383396232352037, 6170031420068042, 28088366503307858
(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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A162054 A067354 A148877 this_sequence A148879 A148880 A148881
Adjacent sequences: A148875 A148876 A148877 this_sequence A148879 A148880 A148881
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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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