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A190647 Continued fraction expansion of Sum_{k>=1} (-1)^k/Fibonacci(k)^2. 1

%I

%S -1,1,4,1,30,1,870,1,9,5,1,12,1,14,1,1,1,1,2,4,1,40,1,9,13,8,35,1,8,3,

%T 1,1,10,4,15,3,1,6,6,1,4,1,4,1,9,6,7,1,4,20,3,2,1,3,1,9,1,2,2,1,1,1,2,

%U 1,1,1,1,3,4,2,18,3,1,1,1,1,1,4,53,4,5,1

%N Continued fraction expansion of Sum_{k>=1} (-1)^k/Fibonacci(k)^2.

%C Borwein et al. express the sum in terms of theta function.

%D J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 203.

%e -0.16753929845562511832413984100914483853736687...

%p with(combinat): with(numtheory): fibcons := add((-1)^k/fibonacci(k)^2,k=1..500): op(cfrac(fibcons,105,'quotients')); # _Nathaniel Johnston_, May 24 2011

%Y Cf. A190648.

%K cofr,sign

%O 0,3

%A _N. J. A. Sloane_, May 16 2011

%E More terms from _Nathaniel Johnston_, May 24 2011

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Last modified September 18 06:07 EDT 2021. Contains 347509 sequences. (Running on oeis4.)