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Search: id:A149454
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| A149454 |
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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), (-1, 1, 1), (0, -1, 1), (1, 0, -1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 13, 49, 198, 822, 3529, 15479, 69033, 311992, 1426666, 6580201, 30587772, 143122551, 673348718, 3183437184, 15113727614, 72019102558, 344308018891, 1650844243543, 7935833965393, 38237726668241, 184631028260387, 893191083199476, 4328485864367581, 21009390791266280, 102121755567680032
(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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + 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: A149452 A140660 A149453 this_sequence A101125 A056275 A149455
Adjacent sequences: A149451 A149452 A149453 this_sequence A149455 A149456 A149457
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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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