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$$a_n=(-2)^{2-n} \sum_{k=0}^{\lfloor\frac{n+1}{2}\rfloor}(-3)^{k-1}\left(\frac{2k}{n+1}-\frac{3}{4}\right) \binom{n+1}{2k}$$求证:$a_n=-a_{n-1}-a_{n-2}$
| $n$ | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20
| | $a_n$ | 1 | -1 | 0 | 1 | -1 | 0 | 1 | -1 | 0 | 1 | -1 | 0 | 1 | -1 | 0 | 1 | -1 | 0 | 1 | -1 | 0 |
$a_n=(-1)^n\left(\frac1{\sqrt3}\sin\left(π n\over3\right) +\cos\left(π n\over3\right)\right)$ |
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