■マルコフ数とフィボナッチ数(その9)

 F1=1,F2=1

 Fn=Fn-1+Fn-2

とすると

 F3=2,F4=3,F5=5,F6=8,F7=13,F8=21,F9=34

 F10=55,F11=89,F12=144,F13=233,・・・

  φ=(1+√5)/2}.−1/φ=(1−√5)/2}

  gn=1/√5{φ^n−(−1/φ)^n}=Fn

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{gn}=1,3,8,21,55,144,・・・

  gn=1/√5{φ^2n−(−1/φ)^2n}=F2n

{gn}=2,8,34,144,・・・

  gn=1/√5{φ^3n−(−1/φ)^3n}=F3n

{gn}=3,21,144,・・・

  gn=1/√5{φ^4n−(−1/φ)^4n}=F4n

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