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A149135
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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, 1, 0), (0, 0, -1), (1, 0, 1)}
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0
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1, 1, 4, 9, 34, 114, 406, 1503, 5592, 21416, 83928, 327244, 1301822, 5202586, 20956424, 85286483, 347725526, 1426195886, 5880016708, 24319110834, 101086632952, 421341186950, 1760919637296, 7383805810480, 31031856064342, 130759597487428, 552246295418526, 2336493297695446, 9905532551587586
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..28.
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[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149132 A149133 A149134 * A149136 A006392 A179079
Adjacent sequences: A149132 A149133 A149134 * A149136 A149137 A149138
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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