20/01/17 23:31:45.00 8XEo1F0J.net
A[n] = A[n-1] + A[n-3] より
A[n] = c･α^n + d･|β|^n･cos(nω+θ),
ここに
α、β、β~ は特性値。 (特性方程式 t^3 - t^2 -1 = 0 の根)
α = {1 + [(29-3√93)/2]^(1/3) + [(29+3√93)/2]^(1/3)}/3
= 1.465571231876768
β = |β| e^(iω),
β~ = |β| e^(-iω),
|β| = 1/(√α) = 0.826031357654187
Re{β} = -(α-1)/2 = -0.232785615938384
cos(ω) = Re{β}/|β| = -0.281812081080629
ω = arg(β) = 1.856478541471303
また、
c^3 - c^2 +(9/31)c -(1/31) = 0,
c = 1/3 + {[4(√31-√27)]^(1/3) + [4(√31 +√27)]^(1/3)}/(3√31)
= 0.6114919919508125
d = (1-c)/cosθ,