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A151173
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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, 0), (1, 1, 0), (1, 1, 1)}
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0
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1, 3, 12, 49, 215, 958, 4382, 20253, 94757, 446425, 2117730, 10094620, 48331541, 232211836, 1119142516, 5407718471, 26190394725, 127097125981, 617874724630, 3008482712483, 14669230148873, 71617201900694, 350046421156296, 1712719416630438, 8388023282558931, 41116009608771585, 201701756272834660
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..26.
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[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: A151170 A151171 A151172 * A301456 A151174 A151175
Adjacent sequences: A151170 A151171 A151172 * A151174 A151175 A151176
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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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