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 A292461 Expansion of (1 - x - x^2 + sqrt((1 - x - x^2)^2 - 4*x^3))/2 in powers of x. 2
 1, -1, -1, -1, -1, -2, -4, -8, -17, -37, -82, -185, -423, -978, -2283, -5373, -12735, -30372, -72832, -175502, -424748, -1032004, -2516347, -6155441, -15101701, -37150472, -91618049, -226460893, -560954047, -1392251012, -3461824644, -8622571758, -21511212261 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA Convolution inverse of A292460. Let f(x) = (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3). G.f.: 1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(1-x-x^2-x^3/(... (continued fraction). G.f.: 1/f(x) = 1 - x - x^2 - x^3*f(x). a(n) = -A292460(n-3) for n > 2. a(n) ~ -sqrt(14*sqrt(5)-30) * phi^(2*n) / (4*sqrt(Pi)*n^(3/2)), where phi is the golden ratio (1+sqrt(5))/2. - Vaclav Kotesovec, Sep 17 2017 MATHEMATICA CoefficientList[Series[(1-x-x^2 +Sqrt[(1-x-x^2)^2 -4*x^3])/2, {x, 0, 50} ], x] (* G. C. Greubel, Aug 13 2018 *) PROG (PARI) x='x+O('x^50); Vec((1-x-x^2 +sqrt((1-x-x^2)^2 -4*x^3))/2) \\ G. C. Greubel, Aug 13 2018 (MAGMA) m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2 +Sqrt((1-x-x^2)^2 -4*x^3))/2)); // G. C. Greubel, Aug 13 2018 CROSSREFS Cf. A203019, A292440, A292460. Sequence in context: A024557 A199409 A025241 * A203019 A004148 A292460 Adjacent sequences:  A292458 A292459 A292460 * A292462 A292463 A292464 KEYWORD sign AUTHOR Seiichi Manyama, Sep 16 2017 STATUS approved

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Last modified January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)