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A151287
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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, -1), (-1, 0), (0, 1), (1, -1), (1, 0)}.
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0
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1, 2, 6, 21, 76, 290, 1148, 4627, 19038, 79554, 336112, 1435522, 6184704, 26838474, 117247440, 515135847, 2274656290, 10090187786, 44940868940, 200897459804, 901082056408, 4053912011322, 18289272082952, 82724956638634, 375064515961744, 1704237546984170, 7759645793395368, 35398085705004882
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: Int(Int(x*(3*x+1)*(-4+Int(2*(1-2*x-15*x^2)^(3/2)*((4*x^2-1)*(92*x^4+76*x^3+43*x^2+6*x+1)*hypergeom([7/4, 9/4],[2],64*x^3*(1+x)/(1-4*x^2)^2)+14*x^3*(10*x+1)*(18*x^3+7*x^2+3*x-1)*hypergeom([9/4, 11/4],[3],64*x^3*(1+x)/(1-4*x^2)^2))/((3*x+1)*(1-4*x^2)^(9/2)*x^2),x))/(1-2*x-15*x^2)^(5/2),x),x)/x^2. - Mark van Hoeij, Aug 16 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[1 + i, j, -1 + n] + aux[1 + i, 1 + 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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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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