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Search: id:A151273
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| A151273 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (1, -1), (1, 1)} |
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+0
1
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| 1, 1, 4, 11, 42, 130, 506, 1701, 6678, 23348, 92162, 330718, 1310042, 4785834, 19002354, 70329169, 279708134, 1045513784, 4163154786, 15682361864, 62502107274, 236910288210, 944854095762, 3599694071586, 14364065086506, 54956626517442, 219388412771714, 842388119494786, 3363960168087706
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A149270 A000296 A032265 this_sequence A149271 A149272 A149273
Adjacent sequences: A151270 A151271 A151272 this_sequence A151274 A151275 A151276
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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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