login
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
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.
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
KEYWORD
cofr,sign
AUTHOR
N. J. A. Sloane, May 16 2011
EXTENSIONS
More terms from Nathaniel Johnston, May 24 2011
STATUS
approved