|
Search: id:A125888
|
|
|
| A125888 |
|
Numerator of sum of first n ratios of Fibonacci to Lucas numbers. |
|
+0
2
|
|
| 0, 1, 4, 11, 95, 1255, 4381, 7662223, 80819870, 3642636055
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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 A., Dec 7, 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.
|
|
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:
0/2, 1/1, 4/3, 11/6, 95/42, 1255/462, 4381/1386, 7662223/1889118, 80819870/17946621, 3642636055/735811461, ...
|
|
CROSSREFS
|
Cf. A000032, A000045.
Sequence in context: A054234 A000850 A004796 this_sequence A055979 A018242 A006248
Adjacent sequences: A125885 A125886 A125887 this_sequence A125889 A125890 A125891
|
|
KEYWORD
|
easy,nonn,frac
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 13 2006
|
|
|
Search completed in 0.002 seconds
|
