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A151329
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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, 1), (-1, 0), (0, 1), (1, -1), (1, 0), (1, 1)}.
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0
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1, 3, 16, 86, 509, 3065, 19088, 120401, 771758, 4991255, 32580974, 214030883, 1414515215, 9392000723, 62625868280, 419056150250, 2812961273801, 18933686864261, 127752378798614, 863851325189957, 5852685174009545, 39721858765234379, 270018313988209400, 1838154015475958213
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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(1+Int((2*x+1)*(5*x+1)*(10+Int(12*(1-2*x-35*x^2)^(3/2)*((1+12*x^2)*(736*x^5+2208*x^4+1096*x^3-44*x^2+44*x+1)*hypergeom([7/4, 9/4],[2],64*(x^2+x+1)*x^2/(1+12*x^2)^2)-7*x*(1824*x^6+2496*x^5+1288*x^4+452*x^3+420*x^2+53*x+10)*hypergeom([9/4, 11/4],[3],64*(x^2+x+1)*x^2/(1+12*x^2)^2))/((5*x+1)*(1+12*x^2)^(9/2)*(2*x+1)^2),x))/(1-2*x-35*x^2)^(5/2),x),x)/((2*x+1)*x). - 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, -1 + j, -1 + n] + aux[-1 + i, j, -1 + 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[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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