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A149823
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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, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}
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0
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1, 2, 4, 10, 28, 82, 260, 848, 2824, 9692, 33728, 119176, 427142, 1544640, 5641356, 20764928, 76923198, 286768066, 1074457916, 4044489594, 15288513274, 58000024522, 220776174294, 842888622120, 3226674092624, 12382733045084, 47625981565686, 183553037038612, 708753109052088, 2741412789264834
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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
| Sequence in context: A094388 A187256 A148110 * A192653 A149824 A202135
Adjacent sequences: A149820 A149821 A149822 * A149824 A149825 A149826
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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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