Difference between revisions of "Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I"
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===Contents=== | ===Contents=== | ||
[[Fibonacci numbers]] <br /> | [[Fibonacci numbers]] <br /> | ||
| + | [[Lucas numbers]]<br /> | ||
| + | [[Sum of Fibonacci numbers]]<br /> | ||
| + | [[Sum of Lucas numbers]]<br /> | ||
| + | [[F(n+1)F(n-1)-F(n)^2=(-1)^n]]<br /> | ||
| + | [[L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)]]<br /> | ||
| + | [[L(n)=F(n+1)+F(n-1)]]<br /> | ||
| + | [[F(2n+1)=F(n+1)^2+F(n)^2]]<br /> | ||
| + | [[F(2n)=F(n+1)^2-F(n-1)^2]]<br /> | ||
| + | [[F(2n)=F(n)L(n)]]<br /> | ||
| + | [[F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)]]<br /> | ||
| + | [[L(n)^2-5F(n)^2=4(-1)^n]]<br /> | ||
| + | [[F(-n)=(-1)^(n+1)F(n)]]<br /> | ||
| + | [[L(-n)=(-1)^nL(n)]]<br /> | ||
[[Category:Paper]] | [[Category:Paper]] | ||
Latest revision as of 00:41, 25 May 2017
S.L. Basin and V.E. Hoggatt, Jr.: A Primer on the Fibonacci Sequence Part I
Published $1963$, The Fibonacci Quarterly.
Online copies
hosted by The Fibonacci Association
Contents
Fibonacci numbers
Lucas numbers
Sum of Fibonacci numbers
Sum of Lucas numbers
F(n+1)F(n-1)-F(n)^2=(-1)^n
L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)
L(n)=F(n+1)+F(n-1)
F(2n+1)=F(n+1)^2+F(n)^2
F(2n)=F(n+1)^2-F(n-1)^2
F(2n)=F(n)L(n)
F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)
L(n)^2-5F(n)^2=4(-1)^n
F(-n)=(-1)^(n+1)F(n)
L(-n)=(-1)^nL(n)
