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Search: id:A151019
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| A151019 |
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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), (-1, 0, 0), (1, 1, 0), (1, 1, 1)} |
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+0
1
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| 1, 2, 10, 32, 160, 584, 2920, 11360, 56800, 229568, 1147840, 4759424, 23797120, 100509824, 502549120, 2152467968, 10762339840, 46606146560, 233030732800, 1018160390144, 5090801950720, 22407240077312, 112036200386560, 496198838730752, 2480994193653760, 11046580426440704, 55232902132203520
(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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A084154 A083099 A032095 this_sequence A004028 A080668 A062453
Adjacent sequences: A151016 A151017 A151018 this_sequence A151020 A151021 A151022
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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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