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Search: id:A149591
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| A149591 |
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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), (0, -1, 0), (0, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 57, 217, 881, 3531, 14669, 61597, 262017, 1119747, 4841949, 21082509, 92245027, 405547121, 1793600501, 7962983781, 35463175171, 158509162139, 710946989375, 3196527500661, 14406394048147, 65098008529837, 294809429733405, 1337492654076381, 6079430868577281, 27685286007842799
(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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, 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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Sequence in context: A149589 A110614 A149590 this_sequence A149592 A149593 A149594
Adjacent sequences: A149588 A149589 A149590 this_sequence A149592 A149593 A149594
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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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