Paper:S.L. Basin/A Primer on the Fibonacci Sequence Part I

{{ #if: |{{{2}}}|S.L. Basin}}{{#if: V.E. Hoggatt, Jr.|{{#if: |, {{ #if: |{{{2}}}|V.E. Hoggatt, Jr.}}{{#if: |, [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]{{#if: |, [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]{{#if: |, [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]] and [[Mathematician:{{{author6}}}|{{ #if: |{{{2}}}|{{{author6}}}}}]]| and [[Mathematician:{{{author5}}}|{{ #if: |{{{2}}}|{{{author5}}}}}]]}}| and [[Mathematician:{{{author4}}}|{{ #if: |{{{2}}}|{{{author4}}}}}]]}}| and [[Mathematician:{{{author3}}}|{{ #if: |{{{2}}}|{{{author3}}}}}]]}}| and {{ #if: |{{{2}}}|V.E. Hoggatt, Jr.}}}}}}: {{#if: |[{{{link}}} A Primer on the Fibonacci Sequence Part I]|A Primer on the Fibonacci Sequence Part I}}{{#if: |, Volume {{{volume}}}}}{{#if: | ({{{ed}}} Edition)}}

{{#if: 1963 |Published {{#if: |${{{day}}}$ {{{month}}} ${{{year}}}$|{{#if: |{{{month}}} ${{{year}}}$|{{#if: |c. ${{{circa}}}$|$1963$}}}}}}{{#if: | {{{era}}}|}}{{#if: The Fibonacci Quarterly |, The Fibonacci Quarterly{{#if: |: ISBN }}}}{{#if: | (translated by [[Mathematician:{{{translated}}}|{{ #if: |{{{2}}}|{{{translated}}}}}]])}}.}}{{#if: |
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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)