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Search: id:A151325
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| A151325 |
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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, 1), (0, 1), (1, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 14, 69, 364, 1964, 10862, 60849, 344914, 1970654, 11336210, 65550856, 380715692, 2219101122, 12974182136, 76050379457, 446774956662, 2629721680448, 15504560993606, 91547835411002, 541254436678564, 3203730923576886, 18982695363209084, 112579789273032820, 668226265440813776
(list; graph; listen)
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OFFSET
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0,2
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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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + 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: A113140 A151324 A121185 this_sequence A020065 A028938 A038213
Adjacent sequences: A151322 A151323 A151324 this_sequence A151326 A151327 A151328
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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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