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A079899
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a(1) = 1; a(n) = Fibonacci(n) - Fibonacci(n-1)* a(n-1) if n > 1.
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0
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1, 0, 2, -1, 8, -32, 269, -3476, 73030, -2482965, 136563164, -12154121452, 1750193489321, -407795083011416, 153738746295304442, -93780635240135708633, 92561486982013944422368, -147820694710276269242519112, 381968675131353879722669389589
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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.
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MATHEMATICA
| t = {1}; gt = 1; For[i = 2, i <= 20, i++, gt = Fibonacci[i] - Fibonacci[i - 1] gt; t = Append[t, gt]]; t
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CROSSREFS
| Sequence in context: A012965 A013119 A012962 * A013327 A009349 A011186
Adjacent sequences: A079896 A079897 A079898 * A079900 A079901 A079902
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KEYWORD
| sign
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 20 2003
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