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A149166
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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), (-1, 1, 0), (1, -1, 1), (1, 1, 0)}
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0
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1, 1, 4, 9, 42, 120, 570, 1825, 8890, 30534, 149418, 536896, 2650062, 9848282, 48696782, 185458037, 920584716, 3576385528, 17767869592, 70107220264, 348996559758, 1395354752334, 6949384790858, 28086919632832, 140041190373276, 571375438865004, 2849662081018354, 11720152721264588, 58492355525303946
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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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + 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, 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: A149165 A083859 A070761 * A149167 A149168 A149169
Adjacent sequences: A149163 A149164 A149165 * A149167 A149168 A149169
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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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