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A079613 F(3*2^n) where F(k) denotes the k-th Fibonacci number. 1
2, 8, 144, 46368, 4807526976, 51680708854858323072, 5972304273877744135569338397692020533504, 79757008057644623350300078764807923712509139103039448418553259155159833079730688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let b = sqrt(5)/5. We have the alternating series identity (10 - 4*sqrt(5))/5 = b/2 - b^2/(2*8) + b^3/(2*8*144) - b^4/(2*8*144*46368) + ..., so this sequence is a generalized Pierce expansion of (10 - 4*sqrt(5))/5 to the base b as defined in A058635. - Peter Bala, Nov 04 2013

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnick, Concrete mathematics, second edition, Addison Wesley, ex. 6.61.

LINKS

Table of n, a(n) for n=0..7.

FORMULA

Sum_{n>=0} 1/a(n) = 5/4 - 1/tau = 0.6319660112... since Sum_{k=0..n} 1/a(k) = 5/4 - F(3*2^n-1)/F(3*2^n).

a(n) = A081976(n+1)*A081976(n+2). - Amarnath Murthy, Apr 03 2003

a(n) = (1/sqrt(5))*( (2 + sqrt(5))^2^n - 1/(2 + sqrt(5))^2^n ) for n >= 1. - Peter Bala, Nov 04 2013

CROSSREFS

Cf. A058635.

Sequence in context: A166356 A009817 A124105 * A091299 A307326 A007314

Adjacent sequences:  A079610 A079611 A079612 * A079614 A079615 A079616

KEYWORD

nonn,changed

AUTHOR

Benoit Cloitre, Jan 29 2003

STATUS

approved

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Last modified November 17 11:02 EST 2019. Contains 329226 sequences. (Running on oeis4.)