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A150453
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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, 0), (0, 0, -1), (0, 1, 0), (1, 1, 1)}
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0
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1, 2, 7, 25, 95, 376, 1523, 6290, 26373, 111886, 479365, 2070771, 9008071, 39423578, 173448057, 766653471, 3402677801, 15158156612, 67751162313, 303735992197, 1365425697699, 6153622483468, 27796881592189, 125830507827952, 570731294883201, 2593415906726304, 11804642094167071, 53817646415676925
(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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A108081 A199247 A116396 * A150454 A150455 A150456
Adjacent sequences: A150450 A150451 A150452 * A150454 A150455 A150456
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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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