已知U1=1,U2=2,求Un=2U(n-2)+U(n-1)+1

Un= 2U(n-2) +U(n-1) +1
Un- 2U(n-1) -1/2= -[U(n-1) -2U(n-2) -1/2 ]
{Un- 2U(n-1) -1/2} 是等比数列 ,q=-1
Un- 2U(n-1) -1/2 = (-1)^(n-2) .(U2- 2U1 -1/2)
=(1/2).(-1)^(n-1)
Un+ (1/6)(-1)^n + 1/2 = 2[ U(n-1) + (1/6)(-1)^n + 1/2]
{Un+ (1/6)(-1)^n + 1/2} 是等比数列,q=2
Un+ (1/6)(-1)^n + 1/2 = 2^(n-1) .(U1+ (1/6)(-1)^1 + 1/2)
= (2/3).2^n
Un = -(1/6)(-1)^n - 1/2 +(2/3).2^n