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A148108
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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, 0), (0, 0, 1), (1, -1, 1), (1, 0, -1)}
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0
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1, 1, 2, 4, 10, 27, 84, 270, 904, 3149, 11221, 41052, 153615, 585423, 2266898, 8899882, 35367261, 142063183, 576212939, 2357624559, 9722575246, 40382761328, 168823553558, 709990487405, 3002235850977, 12759119302740, 54477236422389, 233603326611414, 1005725216037108, 4346070952878284
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
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MATHEMATICA
| 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, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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
| Sequence in context: A138356 A202058 A148107 * A057786 A007776 A123428
Adjacent sequences: A148105 A148106 A148107 * A148109 A148110 A148111
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KEYWORD
| nonn,walk
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AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
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