推 ooopppeeennn:THANK Q ~~~ 03/22 23:28
推 muta22:第二題，看題意an應該不是3n+1吧 @@? 03/23 17:07
→ muta22:用遞迴去作? 03/23 17:08
※ 引述《ooopppeeennn (open)》之銘言：
: 1.Find the mumber of n-digit words generated from the alphabet {0,1,2,3}
: in each of which the number of 0's is even .
: 2.Find the exponential generating function of the sequence
: (1,1*4,1*4*7,1*4*7*...*(3r+1),...).
1. (e^x+e^-x/2)e^xe^xe^x
∞ ∞ ∞
2. A(X)= Σ an x^n = Σ 3n x^n + Σ x^n
n=0 n=0 n=0
1/1-x = Σx^n
1/(1-x)^2 = ΣnX^n-1
x/(1-x)^2 = Σnx^n
3x/(1-x)^2 = Σ3nx^n
A(X) = 3x/(1-x)^2 + 1/1-X
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