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Search: id:A149843
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| A149843 |
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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), (0, 1, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 12, 36, 110, 362, 1212, 4082, 13948, 48522, 169384, 594950, 2109232, 7512468, 26841982, 96379292, 347465634, 1255631188, 4550488168, 16539909198, 60243693028, 219843780960, 803942546000, 2945078921184, 10804509953450, 39698224904260, 146068212217332, 538105375518608, 1984652825246278
(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[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: A010552 A149841 A149842 this_sequence A054542 A117757 A009623
Adjacent sequences: A149840 A149841 A149842 this_sequence A149844 A149845 A149846
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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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