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Search: id:A149137
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| A149137 |
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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), (-1, 0, 1), (1, -1, 0), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 9, 36, 107, 447, 1475, 6348, 22453, 98409, 363883, 1617554, 6174565, 27735580, 108449035, 491170500, 1956865329, 8921660445, 36085841451, 165420054344, 677458847443, 3119736023094, 12910636874207, 59685500134828, 249208756201969, 1155943476497569, 4863700769760251, 22625810378491708
(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, 1 + j, k, -1 + n] + aux[1 + 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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Adjacent sequences: A149134 A149135 A149136 this_sequence A149138 A149139 A149140
Sequence in context: A133125 A126161 A018224 this_sequence A149138 A149139 A149140
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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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