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Search: id:A151318
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| A151318 |
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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), (0, 1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 13, 55, 249, 1131, 5253, 24543, 115825, 549331, 2620029, 12543367, 60270697, 290423355, 1403088885, 6793370415, 32956254945, 160152588195, 779470975725, 3798948989655, 18538237315545, 90565618791435, 442899758973285, 2167985089576575, 10621425660150609, 52078139149834611, 255533719072119133
(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]]; 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: A093834 A033887 A117376 this_sequence A151212 A151213 A102287
Adjacent sequences: A151315 A151316 A151317 this_sequence A151319 A151320 A151321
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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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