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Search: id:A151330
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| A151330 |
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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), (0, 1), (1, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 17, 95, 577, 3591, 22913, 148423, 973297, 6440919, 42938417, 287943719, 1940382241, 13129012247, 89139404337, 606990586023, 4143744218529, 28350360516935, 194338902989281, 1334433092793687, 9176683714637953, 63190999089974583, 435656341477960785, 3006765235738762775
(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[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: A037794 A020056 A086842 this_sequence A010913 A142988 A056660
Adjacent sequences: A151327 A151328 A151329 this_sequence A151331 A151332 A151333
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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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