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Search: id:A151327
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| A151327 |
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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, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 15, 76, 413, 2281, 12889, 73541, 423921, 2458383, 14335834, 83922633, 492956132, 2903156720, 17135951352, 101330250964, 600140389918, 3559105598556, 21131319068601, 125585737386758, 747013179830622, 4446753991483192, 26487831271866795, 157871848076357815, 941434100552046728
(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, 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: A037647 A019477 A019478 this_sequence A125700 A037766 A037654
Adjacent sequences: A151324 A151325 A151326 this_sequence A151328 A151329 A151330
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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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