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Search: id:A151284
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| A151284 |
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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), (0, 1), (1, -1), (1, 0)} |
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+0
1
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| 1, 2, 6, 20, 70, 254, 942, 3550, 13532, 52030, 201386, 783560, 3061442, 12001804, 47181278, 185904220, 733908634, 2901998092, 11490757796, 45552262860, 180762964146, 717939220774, 2853611232902, 11349816190552, 45168339253888, 179845805435900, 716409551285034, 2854926106932244
(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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[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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Adjacent sequences: A151281 A151282 A151283 this_sequence A151285 A151286 A151287
Sequence in context: A000984 A087433 A119373 this_sequence A049138 A095929 A078482
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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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