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Search: id:A149170
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| A149170 |
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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, 1), (1, -1, 1), (1, 1, 0)} |
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+0
1
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| 1, 1, 4, 9, 44, 127, 619, 1989, 9856, 33919, 168677, 607001, 3024616, 11240063, 56097646, 213651441, 1066929850, 4142201763, 20695048729, 81607888787, 407840022294, 1629154166409, 8143064177452, 32884145423379, 164385396321806, 670058403611511, 3349805478222521, 13765134471463579
(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, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A138544 A093149 A048054 this_sequence A024053 A048892 A108849
Adjacent sequences: A149167 A149168 A149169 this_sequence A149171 A149172 A149173
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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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