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A190647 Continued fraction expansion of Sum_{k>=1} (-1)^k/Fibonacci(k)^2. 1
-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, 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, 1, 1, 1, 1, 3, 4, 2, 18, 3, 1, 1, 1, 1, 1, 4, 53, 4, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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.

LINKS

Table of n, a(n) for n=0..81.

EXAMPLE

-0.16753929845562511832413984100914483853736687...

MAPLE

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

CROSSREFS

Cf. A190648.

Sequence in context: A226936 A073323 A077097 * A123126 A303277 A174501

Adjacent sequences:  A190644 A190645 A190646 * A190648 A190649 A190650

KEYWORD

cofr,sign

AUTHOR

N. J. A. Sloane, May 16 2011

EXTENSIONS

More terms from Nathaniel Johnston, May 24 2011

STATUS

approved

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Last modified July 29 01:22 EDT 2021. Contains 346340 sequences. (Running on oeis4.)