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A148931
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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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 1, 0)}
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0
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1, 1, 3, 9, 28, 96, 331, 1178, 4277, 15668, 58207, 217827, 820822, 3113057, 11858060, 45369618, 174201971, 670880989, 2590897603, 10028967336, 38902441680, 151185031351, 588509650239, 2294305412573, 8956328591359, 35005542995118, 136969955527081, 536476427847843, 2103186073322950
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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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A014323 A000752 A047027 * A148932 A151421 A148933
Adjacent sequences: A148928 A148929 A148930 * A148932 A148933 A148934
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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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