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Search: id:A151320
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| A151320 |
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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, 0), (0, 1), (1, -1), (1, 0), (1, 1)} |
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+0
1
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| 1, 3, 13, 58, 270, 1280, 6150, 29805, 145360, 712206, 3501803, 17264747, 85302729, 422197260, 2092558843, 10383452493, 51573082768, 256362474771, 1275210602985, 6346900307554, 31605149836728, 157449319326981, 784667701737738, 3911759095866487, 19506630908252765, 97297440023869383
(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, 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: A151224 A151225 A151226 this_sequence A151227 A151228 A152594
Adjacent sequences: A151317 A151318 A151319 this_sequence A151321 A151322 A151323
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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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