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Search: id:A151289
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| A151289 |
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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, 1), (1, 0), (1, 1)} |
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+0
1
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| 1, 2, 7, 21, 80, 267, 1042, 3655, 14400, 51960, 205770, 756169, 3003754, 11179972, 44496878, 167181919, 666257284, 2521360818, 10057256094, 38278262216, 152783755958, 584199222356, 2332875408218, 8954456162165, 35770374449310, 137743370071244, 550391555936678, 2125263063052980
(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]]; 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: A126133 A127540 A060900 this_sequence A150300 A150301 A150302
Adjacent sequences: A151286 A151287 A151288 this_sequence A151290 A151291 A151292
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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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