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A125888 Numerator of sum of first n ratios of Fibonacci to Lucas numbers. 1
0, 1, 4, 11, 95, 1255, 4381, 145067, 7662223, 80819870, 3642636055, 790371794974, 19684652229146, 11040403321665367, 3322851650570694710, 219687751171273292755, 515022606093026805779903, 1946889068386887991263046319, 659536996247168335462717076503 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A125889(n) = denominator(SUM[i=1..n]F(i)/L(i)) = SUM[i=1..n] A000045(i)/A000032(i) = n/sqrt(5) + O(1). - Max Alekseyev, Dec 07 2006

denominator(SUM[i=1..n]A000045(i)/A000032(i)).

GCD(F(i),L(i)) <= 2, so the ratio reduces when there is a factor of two in common, every third term. Example as continued fraction: 0 + 1+1/3+2/4+3/7+5/11+8/18+13/29+21/47+34/76+55/123 = 1/1+ 1/19+ 1/4+ 1/1+ 1/13+ 1/2+ 1/4+ 1/1+ 1/6+ 1/6+ 1/1+ 1/85+ 1/1+ 1/4+ 1/2.

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = numerator(SUM[i=1..n]F(i)/L(i)) = numerator(SUM[i=1..n]A000045(i)/A000032(i)).

EXAMPLE

The fractions, reduced to lowest terms, begin:

0/1, 1/1, 4/3, 11/6, 95/42, 1255/462, 4381/1386, 145067/40194, 7662223/1889118, 80819870/17946621, 3642636055/735811461, ...

CROSSREFS

Cf. A000032, A000045.

Sequence in context: A004796 A181267 A280036 * A266894 A144744 A267154

Adjacent sequences:  A125885 A125886 A125887 * A125889 A125890 A125891

KEYWORD

easy,nonn,frac

AUTHOR

Jonathan Vos Post, Dec 13 2006

STATUS

approved

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Last modified December 13 09:05 EST 2017. Contains 295957 sequences.