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Search: id:A151278
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| A151278 |
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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, 0)} |
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+0
1
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| 1, 2, 4, 10, 26, 66, 178, 488, 1320, 3674, 10318, 28728, 81344, 231634, 655614, 1876510, 5391998, 15423550, 44473310, 128605264, 370583896, 1074340126, 3121406738, 9043275450, 26324579482, 76763009234, 223318464418, 652169185724, 1907256905140, 5566743069850, 16299205388766, 47779358006460
(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[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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Sequence in context: A055775 A090032 A090377 this_sequence A149810 A095337 A162533
Adjacent sequences: A151275 A151276 A151277 this_sequence A151279 A151280 A151281
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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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