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Search: id:A150030
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| A150030 |
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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), (-1, 1, 0), (1, 0, 0), (1, 0, 1)} |
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+0
1
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| 1, 2, 6, 16, 62, 209, 826, 2884, 12299, 46495, 197275, 752364, 3328340, 13257631, 58135717, 231929737, 1046257805, 4296230064, 19202622824, 78758167294, 359644608451, 1506796125323, 6819578915478, 28503632171786, 131253674953941, 557875859380520, 2547299431112866, 10794901911340637
(list; graph; listen)
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OFFSET
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0,2
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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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 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
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Sequence in context: A027742 A033301 A093113 this_sequence A150031 A121753 A150032
Adjacent sequences: A150027 A150028 A150029 this_sequence A150031 A150032 A150033
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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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