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Search: id:A148469
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| A148469 |
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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, 0), (-1, 0, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)} |
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+0
1
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| 1, 1, 2, 6, 19, 63, 233, 881, 3454, 13895, 56957, 237185, 1001514, 4274113, 18421481, 80049553, 350339864, 1543114276, 6834599858, 30421512784, 136016594930, 610563182006, 2750696838904, 12433236054068, 56366827142938, 256245427672152, 1167838731186473, 5334787378301284, 24422180784557641
(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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A063030 A148467 A148468 this_sequence A151283 A119370 A069728
Adjacent sequences: A148466 A148467 A148468 this_sequence A148470 A148471 A148472
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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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