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A150968
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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, 0), (0, 1, -1), (1, 0, 1), (1, 1, 1)}
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0
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1, 2, 9, 36, 155, 711, 3252, 14987, 71034, 335301, 1590682, 7638914, 36642619, 176197696, 853153680, 4128974864, 20015103523, 97433641619, 474259672053, 2311057339844, 11293164676456, 55188713180901, 269929241371606, 1322783339929551, 6483263066793933, 31796814951934582, 156163700094061499
(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[1 + i, -1 + j, 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: A150967 A121769 A006782 * A073156 A150969 A150970
Adjacent sequences: A150965 A150966 A150967 * A150969 A150970 A150971
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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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