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 A079899 a(1) = 1; a(n) = Fibonacci(n) - Fibonacci(n-1)* a(n-1) if n > 1. 0
 1, 0, 2, -1, 8, -32, 269, -3476, 73030, -2482965, 136563164, -12154121452, 1750193489321, -407795083011416, 153738746295304442, -93780635240135708633, 92561486982013944422368, -147820694710276269242519112, 381968675131353879722669389589 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 29 03:55 EDT 2023. Contains 365750 sequences. (Running on oeis4.)