OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: ((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1 -4*x^2 - x^4)). - David Callan, Jan 17 2016
Conjecture D-finite with recurrence n*a(n) -2*a(n-1) +(-11*n+20)*a(n-2) +14*a(n-3) +(39*n-152)*a(n-4) -22*a(n-5) +(-41*n+268)*a(n-6) -6*a(n-7) +12*(-n+6)*a(n-8)=0. - R. J. Mathar, Jan 13 2023
a(n) ~ ((1 + (-1)^n)*phi^(3/2) + 2*(1 - (-1)^n)) * phi^((3*n + 1)/2) / (2*sqrt(5)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Mar 08 2023
MATHEMATICA
CoefficientList[Normal[Series[((1-3x^2)Sqrt[(1+2x)/(1-2x)] +(1 + 2x)(1+ x^2))/(2(1-4x^2-x^4)), {x, 0, 40}]], x] (* David Callan, Jan 17 2016 *)
PROG
(PARI) my(x='x+O('x^40)); Vec(((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4))) \\ G. C. Greubel, Jul 16 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( ((1 -3*x^2)*Sqrt((1+2*x)/(1-2*x)) +(1+2*x)*(1+x^2))/(2*(1-4*x^2-x^4)) )); // G. C. Greubel, Jul 16 2019
(Sage) (((1-3*x^2)*sqrt((1+2*x)/(1-2*x)) + (1+2*x)*(1+x^2))/(2*(1-4*x^2 - x^4))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 16 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved