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Search: id:A151409
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| A151409 |
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Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (0, 1), (1, -1), (1, 1)} |
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+0
1
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| 1, 1, 2, 5, 14, 39, 116, 364, 1154, 3712, 12245, 40940, 137779, 468927, 1612511, 5576133, 19394557, 67912071, 238967041, 844127643, 2994719855, 10665904225, 38103524211, 136531060288, 490663266986, 1767779916316, 6383507664304, 23102978335829, 83786075774791, 304420859569058, 1108009834275929
(list; graph; listen)
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OFFSET
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0,3
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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.
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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, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A105641 A027035 A102406 this_sequence A003054 A148316 A148317
Adjacent sequences: A151406 A151407 A151408 this_sequence A151410 A151411 A151412
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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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