■フィボナッチ数・リュカ数の問題(その11)
F0=0,F1=1
0,1,1,2,3,5,8,13,21,34,55,89,144,・・・
Fn=1/√5・{τ^n-(-τ)^-n}
L0=2,L1=1
2,1,3,4,7,11,18,29,47,76,123,・・・
Ln={τ^n+(-τ)^-n}
G0=p,G1=q
Gn=Gn-1+Gn-2
Gn+1=pFn+qFn+1
T0=0,T1=0,T2=1
Tn=Tn-1+Tn-2+Tn-3
α=1/3・{(19+3√33)^1/3+(19-3√33)^1/3+1}=1.839287・・・
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F2n+1=(Fn+1)^2+(Fn)^2
Fn+2Fn-1=(Fn+1)^2-(Fn)^2
Fn+1Fn-1-(Fn)^2=(-1)^n
Fn=FmFn+1-m+Fm-1Fn-m
Ln+m+(-1)^mLn-m=LmLn
L2n+2(-1)^2=(Ln)^2
Ln-1+Ln+1=5Fn
Fn-1+Fn+1=Ln
Fn+2-Fn-2=Ln
Fn+Ln=2Fn+1
F2n=FnLn
Fn+1Ln+1-FnLn=F2n+1
Fn+m+(-1)^nFn-m=LmFn
Fn+m-(-1)^nFn-m=FmLn
LmFn+LnFm=2Fn+2
LmFn-LnFm=(-1)^m2Fn-2
Lm+n-(-1)^mLn-m=5FmFn
(Ln)^2-2L2n=-5(Fn)^2
L2n-2(-1)^2=5(Fn)^2
5(Fn)^2-(Ln)^2=4(-1)^n+1*****
3Fn+Ln=2Fn+2
5Fn+3Ln=2Ln+2
Ln=Fn+2+2Fn-1
Ln=L1Fn+L0Fn-1
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