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A151366
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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, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0)}
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0
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1, 0, 2, 2, 12, 30, 130, 462, 1946, 7980, 34776, 153120, 694056, 3194334, 14971242, 71133062, 342500730, 1667918824, 8208038124, 40772105244, 204270936480, 1031413134960, 5245260798960, 26850869456400, 138289429433200, 716247599547360, 3729128330979200, 19510354349803200, 102540704879774160
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..28.
M. Bousquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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FORMULA
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G.f. ((2*x+1)*(hypergeom([-2/3, -1/3],[1],27*x^2*(2*x+1))+4*x*hypergeom([-1/3, 1/3],[2],27*x^2*(2*x+1)))/(3*x+1)-1-3*x-5*x^2)/(3*x^3). - Mark van Hoeij, Aug 17 2014
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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[i, 1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]
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CROSSREFS
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Sequence in context: A130306 A199127 A093044 * A184944 A033886 A185144
Adjacent sequences: A151363 A151364 A151365 * A151367 A151368 A151369
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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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