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(PARI) t='t+O('t^50); Vec((1-t^2+2t2*t^3)/(1-2t2*t-2t2*t^2+2t2*t^3+t^4)) \\ G. C. Greubel, Jul 05 2017
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G.f.: g(t) = (1-t^2+2*t^3)/(1-2*t-2*t^2+2*t^3+t^4).
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reviewed
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fract((1+sqrt(2))^n)) = (1/2)*(1+(-1)^n)-(-1)^n*(1+sqrt(2))^(-n) = (1/2)*(1+(-1)^n)-(1-sqrt(2))^n.
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