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A150935
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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, 0, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}
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0
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1, 2, 9, 33, 159, 671, 3288, 14719, 72664, 335880, 1664988, 7849149, 39004188, 186294948, 927213201, 4469530443, 22269520555, 108073079585, 538890342551, 2628561459138, 13114310579949, 64221071659033, 320544468838524, 1574624610642784, 7861912554105647, 38717644728189914, 193361258767889412
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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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150932 A150933 A150934 * A150936 A109719 A212348
Adjacent sequences: A150932 A150933 A150934 * A150936 A150937 A150938
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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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