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Search: id:A149589
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| A149589 |
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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, 0, 1), (-1, 1, 1), (0, 0, -1), (1, 1, 1)} |
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+0
1
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| 1, 1, 5, 15, 57, 205, 809, 3119, 12409, 49395, 200319, 813021, 3331245, 13694535, 56693979, 235293123, 981003705, 4101098479, 17208126251, 72362389463, 305135947291, 1289321950797, 5460592598361, 23167024483265, 98473820236213, 419231162422567, 1787703023731091, 7633637858431371
(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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A137959 A001552 A165731 this_sequence A110614 A149590 A149591
Adjacent sequences: A149586 A149587 A149588 this_sequence A149590 A149591 A149592
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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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