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A151314
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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), (0, 1), (1, -1), (1, 1)}.
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0
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1, 2, 11, 49, 277, 1479, 8679, 49974, 301169, 1805861, 11097563, 68225081, 425527103, 2660509721, 16787151965, 106242633509, 676589551793, 4321724272449, 27729861453735, 178418992948065, 1151938855186131, 7455729526078989, 48388319643548481, 314727421388892459, 2051665321667625351
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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)*(-2+Int(6*(1-2*x-35*x^2)^(3/2)*((1+12*x^2)*(1808*x^5+1084*x^4+540*x^3+107*x^2-132*x-5)*hypergeom([7/4, 9/4],[2],64*(x^2+x+1)*x^2/(1+12*x^2)^2)-14*x*(636*x^6+2104*x^5+811*x^4-500*x^3-403*x^2-55*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)/((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, 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] + 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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