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A148924
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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, 0), (0, 1, 1), (1, -1, 0), (1, 0, -1)}
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0
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1, 1, 3, 9, 27, 89, 305, 1059, 3745, 13479, 49087, 180213, 666995, 2486247, 9317763, 35090553, 132721777, 503845539, 1919019473, 7330426325, 28075074671, 107777969567, 414624345139, 1598154664693, 6170822888835, 23865066734975, 92431451211199, 358477967010287, 1392025778093215, 5411688536261939
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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..29.
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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A151029 A179263 A147242 * A113994 A217639 A148925
Adjacent sequences: A148921 A148922 A148923 * A148925 A148926 A148927
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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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