A079899 a(1) = 1; a(n) = Fibonacci(n) - Fibonacci(n-1)* a(n-1) if n > 1.

1, 0, 2, -1, 8, -32, 269, -3476, 73030, -2482965, 136563164, -12154121452, 1750193489321, -407795083011416, 153738746295304442, -93780635240135708633, 92561486982013944422368, -147820694710276269242519112, 381968675131353879722669389589

Offset

1,3

Comments

1. Let s(n) be a sequence such that lim s(n)/s(n+1) = K different from -1. The "oscillator sequence" (or simply "oscillator") of s(n) is the sequence s'(n) defined by the rules: s'(1) = 1; s'(n) = 1 - (s(n-1)/s(n)) s'(n-1). 2. It is an open problem whether the oscillator (prime)' converges to 1/2 or diverges. 3. s'(n) = 1 - (s(n-1)/s(n)) s'(n-1) = [s(n) - s(n-1) s'(n-1)]/s(n). The numerator is the expression s(n) - s(n-1) s'(n-1), which motivates the definition of the above sequence a(n). a(n) is called the "integral oscillator" of Fibonacci(n). In general the integral oscillator of s(n) can be defined similarly.

Links

Table of n, a(n) for n=1..19.

Mathematica

t = {1}; gt = 1; For[i = 2, i <= 20, i++, gt = Fibonacci[i] - Fibonacci[i - 1] gt; t = Append[t, gt]]; t

Crossrefs

Sequence in context: A013119 A012962 A214731 * A333469 A239444 A224090

Adjacent sequences: A079896 A079897 A079898 * A079900 A079901 A079902

Keyword

sign

Author

Joseph L. Pe, Feb 20 2003

Status

approved