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Search: id:A151308
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| A151308 |
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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, 0), (1, 1)} |
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+0
1
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| 1, 2, 9, 34, 161, 690, 3340, 15127, 74025, 345350, 1700641, 8078534, 39940239, 191998427, 951780628, 4613430423, 22912945993, 111732959607, 555692292248, 2722027662579, 13551646056826, 66612271878273, 331891009874753, 1635825684723348, 8155387103254651, 40283455920402930, 200930087609072285
(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[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: A150942 A150943 A150944 this_sequence A140217 A032601 A083141
Adjacent sequences: A151305 A151306 A151307 this_sequence A151309 A151310 A151311
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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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