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Search: id:A149824
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| A149824 |
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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, 0), (1, 0, 0), (1, 1, -1)} |
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+0
1
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| 1, 2, 4, 10, 28, 82, 276, 950, 3310, 12078, 44530, 166938, 643884, 2497582, 9846816, 39300510, 157864202, 640945466, 2623007032, 10794098482, 44800697192, 186807264986, 783544937362, 3303567503730, 13988690095946, 59491279201242, 254085592304632, 1088721319725422, 4683544234743224
(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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A094388 A148110 A149823 this_sequence A068875 A135336 A149825
Adjacent sequences: A149821 A149822 A149823 this_sequence A149825 A149826 A149827
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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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