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Search: id:A149872
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| A149872 |
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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), (-1, 1, -1), (1, 0, 0), (1, 0, 1)} |
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+0
1
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| 1, 2, 5, 13, 42, 138, 491, 1691, 6506, 24158, 95110, 359634, 1476071, 5814658, 24038501, 95389250, 405330287, 1652139456, 7033071180, 28753343889, 124893383967, 520653084842, 2260016606059, 9429634274366, 41586641260308, 176164600968080, 775437292036982, 3283769720054476, 14645257640355143
(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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + 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: A149869 A149870 A149871 this_sequence A149873 A149874 A114297
Adjacent sequences: A149869 A149870 A149871 this_sequence A149873 A149874 A149875
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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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