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A151181
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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, 0, 1), (0, 1, 1), (1, 0, 1), (1, 1, -1)}
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0
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1, 3, 12, 50, 230, 1059, 5043, 24073, 116650, 566294, 2770564, 13575457, 66809023, 329196128, 1626369177, 8042962723, 39842574055, 197525771175, 980382103175, 4869026293964, 24201218678644, 120351728434595, 598854576465375, 2981035269045935, 14845798328053850, 73957590749549226, 368560458686376624
(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, -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]]; 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: A191242 A105479 A151180 * A094601 A009024 A043291
Adjacent sequences: A151178 A151179 A151180 * A151182 A151183 A151184
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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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