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Search: id:A149041
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| A149041 |
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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, 1, 0), (0, 1, 1), (1, -1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 3, 10, 36, 137, 553, 2285, 9693, 41855, 183561, 814876, 3654604, 16535384, 75366335, 345737195, 1594970323, 7394406989, 34431368556, 160953486204, 755038939596, 3553119378943, 16768513088521, 79343597203618, 376326378568765, 1788822334786162, 8520094632728376, 40656455487711977
(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, 1 + k, -1 + n] + aux[-1 + i, 1 + 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, -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
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Sequence in context: A129156 A171753 A002212 this_sequence A129247 A162162 A149042
Adjacent sequences: A149038 A149039 A149040 this_sequence A149042 A149043 A149044
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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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