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Search: id:A151322
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| A151322 |
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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), (-1, 0), (0, 1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 14, 65, 330, 1683, 8874, 47088, 253802, 1375939, 7524651, 41346061, 228447273, 1267005772, 7054307476, 39394861448, 220641191059, 1238773724011, 6970910527593, 39305772011050, 222039381179593, 1256404002028860, 7120347445063067, 40409910873522737, 229639109317630051, 1306567259328079561
(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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 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: A161131 A026592 A034275 this_sequence A002320 A151323 A113140
Adjacent sequences: A151319 A151320 A151321 this_sequence A151323 A151324 A151325
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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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