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A148012
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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, 0, 1), (-1, 1, -1), (1, -1, -1), (1, 0, 0)}
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0
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1, 1, 2, 3, 8, 15, 44, 101, 348, 859, 2926, 7765, 28092, 77797, 288226, 835551, 3149704, 9376877, 36183832, 110801091, 431609988, 1350519440, 5338560871, 17003928647, 67861860571, 219953201097, 885178666480, 2907032661937, 11800981627623, 39264792923311, 160349091607954, 539475559104643, 2217553429366461
(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, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A148009 A148010 A148011 * A161178 A006882 A080498
Adjacent sequences: A148009 A148010 A148011 * A148013 A148014 A148015
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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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