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國立臺灣大學 2022 · 考試 · 第 3 題

(10%) The generating function in partial fraction decomposition for the recurrence equation $a_n = -a_{n-1} + 6a_{n-2}$ for $a_n$ in terms of $a_0 = A$ and $a_1 = B$ is:

(A)
$\frac{1}{5}\left[\frac{2A+B}{1-3x} + \frac{3A-B}{1+2x}\right]$
(B)
$\frac{1}{5}\left[\frac{2A+B}{1-3x} + \frac{3A+B}{1+2x}\right]$
(C)
$\frac{1}{5}\left[\frac{2A-B}{1-3x} + \frac{3A-B}{1+2x}\right]$
(D)
$\frac{1}{5}\left[\frac{3A-B}{1-2x} + \frac{2A-B}{1+3x}\right]$
(E)
$\frac{1}{5}\left[\frac{3A+B}{1-2x} + \frac{2A-B}{1+3x}\right]$

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