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A151175
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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
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1, 3, 12, 49, 219, 971, 4517, 20771, 98450, 461981, 2213354, 10519245, 50753596, 243307767, 1179762984, 5690972110, 27696647862, 134229569535, 655129908566, 3186566575192, 15587994181738, 76039623155226, 372662021788428, 1822155305407466, 8944059110331015, 43817771192888596, 215363155240618719
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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[-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: A151173 A301456 A151174 * A151176 A151177 A344419
Adjacent sequences: A151172 A151173 A151174 * A151176 A151177 A151178
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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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