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Search: id:A149857
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| A149857 |
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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), (0, 0, 1), (0, 1, -1), (1, 0, 0)} |
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+0
1
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| 1, 2, 5, 13, 38, 116, 373, 1212, 4063, 13790, 47820, 166683, 589544, 2096696, 7543287, 27220425, 99068066, 361665420, 1329801449, 4899090442, 18150085724, 67373439992, 251310896362, 938695649224, 3520154347595, 13218509615238, 49811826743912, 187895224773770, 710859105078058, 2692016339593940
(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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A149856 A064384 A148302 this_sequence A001475 A149858 A148303
Adjacent sequences: A149854 A149855 A149856 this_sequence A149858 A149859 A149860
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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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