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

-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

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: A073323 A350759 A077097 * A353792 A123126 A303277

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