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Search: id:A149122
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| A149122 |
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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, -1), (1, -1, 0), (1, 1, 1)} |
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+0
1
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| 1, 1, 4, 9, 34, 94, 368, 1131, 4466, 14468, 57356, 193200, 767664, 2650814, 10552660, 37141229, 148040634, 528844796, 2109494072, 7623040680, 30426290940, 110998813606, 443245452212, 1629794707352, 6510278089072, 24096191513060, 96278729708172, 358370832690704, 1432209340089340, 5357082370310378
(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, k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A054433 A096531 A149121 this_sequence A149123 A149124 A149125
Adjacent sequences: A149119 A149120 A149121 this_sequence A149123 A149124 A149125
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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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