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Search: id:A149822
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| A149822 |
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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, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 10, 28, 80, 263, 895, 2980, 10574, 38446, 137922, 517383, 1968961, 7397211, 28703778, 112553640, 436450450, 1734871068, 6950344298, 27575805457, 111606728461, 454473446902, 1834842685486, 7530466453251, 31059053298538, 127126679057165, 527605282606956, 2198623174582533
(list; graph; listen)
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OFFSET
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0,2
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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, 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, 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: A149819 A149820 A149821 this_sequence A034472 A094388 A148110
Adjacent sequences: A149819 A149820 A149821 this_sequence A149823 A149824 A149825
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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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