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Search: id:A149425
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| A149425 |
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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, 0, 0), (0, -1, 0), (0, 1, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 4, 13, 42, 146, 520, 1893, 6928, 25520, 95258, 357332, 1348314, 5109674, 19419422, 74124571, 283750244, 1089053340, 4189218564, 16143369610, 62342218516, 241154261642, 934254937426, 3624326380994, 14076738707662, 54742699821140, 213116870712502, 830503102890218, 3239368922556944
(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, 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: A010900 A070031 A082989 this_sequence A047144 A072307 A121486
Adjacent sequences: A149422 A149423 A149424 this_sequence A149426 A149427 A149428
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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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