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Search: id:A148447
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| A148447 |
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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, 0, 0), (-1, 0, 1), (0, 1, 1), (1, 0, -1)} |
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+0
1
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| 1, 1, 2, 6, 17, 50, 171, 567, 1986, 7141, 25843, 96251, 361442, 1374276, 5293874, 20516616, 80360955, 316699197, 1256415912, 5016548166, 20123158508, 81163144236, 328709365541, 1336843859193, 5457904253914, 22356889879962, 91891356641343, 378782930930332, 1565838304801996, 6489933891530336
(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, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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
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Sequence in context: A027914 A098703 A025272 this_sequence A148448 A148449 A148450
Adjacent sequences: A148444 A148445 A148446 this_sequence A148448 A148449 A148450
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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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