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Search: id:A148089
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| A148089 |
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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, 0, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 4, 10, 24, 69, 193, 590, 1764, 5563, 17405, 56664, 183567, 610476, 2021736, 6829184, 23033270, 78880450, 269888858, 933922349, 3230929825, 11279210350, 39390678315, 138553842436, 487618273180, 1725964559833, 6113971964633, 21760644309885, 77519044920785, 277226106750016, 992352935678065
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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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[i, j, -1 + 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: A028506 A148088 A029893 this_sequence A060776 A061055 A148090
Adjacent sequences: A148086 A148087 A148088 this_sequence A148090 A148091 A148092
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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