

A153387


Decimal expansion of Sum_{n>=1} 1/Fibonacci(2*n1).


8



1, 8, 2, 4, 5, 1, 5, 1, 5, 7, 4, 0, 6, 9, 2, 4, 5, 6, 8, 1, 4, 2, 1, 5, 8, 4, 0, 6, 2, 6, 7, 3, 2, 8, 1, 7, 3, 3, 2, 1, 8, 9, 3, 5, 4, 2, 6, 6, 0, 8, 2, 9, 9, 2, 3, 2, 6, 0, 2, 9, 0, 1, 5, 0, 1, 9, 4, 0, 8, 3, 0, 4, 0, 3, 6, 7, 7, 7, 3, 9, 6, 7, 5, 9, 8, 9, 1, 3, 8, 9, 9, 8, 1, 9, 8, 2, 0, 7, 5, 0, 7, 6, 4, 2, 4
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OFFSET

1,2


COMMENTS

Borwein et al. express the sum in terms of theta functions.  N. J. A. Sloane, May 16 2011


REFERENCES

J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See pp. 202203.


LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1000
Joerg Arndt, On computing the generalized Lambert series, arXiv:1202.6525v3 [math.CA], (2012).


FORMULA

Equals sqrt(5)/4 * (T(b^2)^2  T(b)^2) where T(q) = 1 + 2*sum(n>=1, q^(n^2) ) and b = 1/2*(1sqrt(5)); see the Arndt reference and the references cited there.  Joerg Arndt, Feb 01 2014


EXAMPLE

1.8245151574069245681...


CROSSREFS

Cf. A079586, A153386, A190649.
Sequence in context: A019775 A274211 A138499 * A010520 A169847 A285299
Adjacent sequences: A153384 A153385 A153386 * A153388 A153389 A153390


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Dec 25 2008


EXTENSIONS

Definition reconciled to sequence and example by Clark Kimberling, Aug 06 2013


STATUS

approved



