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Search: id:A148161
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| A148161 |
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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, 1, -1), (1, 0, 0)} |
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+0
1
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| 1, 1, 2, 4, 11, 31, 86, 262, 787, 2442, 7677, 24581, 80379, 261809, 867313, 2890472, 9684442, 32683354, 110898717, 379064856, 1297810439, 4466393711, 15433476163, 53483388756, 185962286216, 648576840593, 2269821822857, 7957275602226, 27969780462858, 98546712605786, 347890004162970, 1230552458589243
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
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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[i, -1 + 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
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Sequence in context: A034770 A002387 A148160 this_sequence A148162 A148163 A039300
Adjacent sequences: A148158 A148159 A148160 this_sequence A148162 A148163 A148164
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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