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Search: id:A151283
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| A151283 |
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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)} |
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+0
1
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| 1, 2, 6, 19, 64, 223, 795, 2885, 10605, 39385, 147476, 555912, 2107242, 8025186, 30685270, 117733427, 453071613, 1748121379, 6760511585, 26198611791, 101712113508, 395531586276, 1540401288244, 6007173448533, 23455099384509, 91683043012353, 358744056768580, 1405039139709542, 5507673913262840
(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[-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: A148467 A148468 A148469 this_sequence A119370 A069728 A150083
Adjacent sequences: A151280 A151281 A151282 this_sequence A151284 A151285 A151286
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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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