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Search: id:A149812
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| A149812 |
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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, 0, 1), (1, 0, 0)} |
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+0
1
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| 1, 2, 4, 10, 26, 71, 213, 656, 2043, 6510, 21185, 69751, 232653, 785663, 2669329, 9132465, 31519477, 109446096, 381688232, 1337901064, 4711210673, 16648931593, 59052004172, 210185465527, 750190870068, 2684593024346, 9633007467277, 34647424892614, 124875717433200, 451000306659001, 1631969490627470
(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, 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: A035079 A106221 A149811 this_sequence A149813 A149814 A125108
Adjacent sequences: A149809 A149810 A149811 this_sequence A149813 A149814 A149815
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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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