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A149814
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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), (-1, -1, 1), (-1, 1, -1), (0, 0, 1), (1, 0, 0)}
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0
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1, 2, 4, 10, 26, 71, 229, 758, 2465, 8326, 28723, 99984, 360520, 1319152, 4795180, 17632228, 66029313, 248365358, 941304113, 3599515826, 13781394242, 52987143192, 205844656410, 802871708059, 3136100869461, 12309556579260, 48513612043129, 191637213524949, 760513553352670, 3028212093106559
(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, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A149811 A149812 A149813 * A125108 A075864 A180023
Adjacent sequences: A149811 A149812 A149813 * A149815 A149816 A149817
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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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