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A148000
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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, -1), (0, 0, 1), (1, 0, -1)}
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0
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1, 1, 2, 3, 8, 15, 39, 87, 254, 633, 1755, 4817, 13683, 38328, 109188, 327645, 962488, 2855001, 8585783, 26100683, 79038683, 239634748, 749702378, 2323224093, 7216147407, 22570101754, 71214487008, 224091470121, 704212414119, 2258037023357, 7208557781173, 23017651439589, 73774471716580
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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
| Sequence in context: A049957 A151255 A147999 * A148001 A148002 A148003
Adjacent sequences: A147997 A147998 A147999 * A148001 A148002 A148003
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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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