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A148111
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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, 0, 1), (0, 1, -1), (1, -1, 0), (1, 0, 0)}
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0
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1, 1, 2, 4, 10, 29, 81, 254, 808, 2662, 9199, 31691, 113292, 411434, 1508096, 5655391, 21312822, 81456715, 315068989, 1224636405, 4817113618, 19064234579, 75937817010, 304996020184, 1230021324817, 4993203500709, 20378945659090, 83498766348274, 344019854358410, 1422622942166198, 5906293065080430
(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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A153921 A189582 A060315 * A148112 A148113 A005505
Adjacent sequences: A148108 A148109 A148110 * A148112 A148113 A148114
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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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