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A151337
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Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, 1), (1, -1)}
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0
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1, 0, 0, 1, 2, 1, 11, 27, 60, 216, 724, 1976, 7140, 23723, 78257, 273707, 965000, 3354664, 12105626, 43619606, 158328834, 581558532, 2150453882, 7986765356, 29926146152, 112632743114, 426211686362, 1621337531160, 6195825999752, 23775419983051, 91628399336871, 354427790698043, 1375944479482008, 5359864838951956
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OFFSET
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0,5
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LINKS
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Table of n, a(n) for n=0..33.
A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 31, Tag 36.
M. Bousquet-Mélou 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[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A111724 A184299 A080371 * A013019 A012904 A013015
Adjacent sequences: A151334 A151335 A151336 * A151338 A151339 A151340
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KEYWORD
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nonn,walk
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AUTHOR
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Manuel Kauers, Nov 18 2008
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STATUS
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approved
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