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Re:递推公式 a[i]=2(a[i-1]+a[i-2](i-1)) ?

Posted by demo at 2009-05-18 21:21:57 on Problem 3734
In Reply To:Re:递推公式 a[i]=2*(a[i-1]+a[i-2]*(i-1)) ? Posted by:19880901 at 2009-05-17 19:15:47

    n/2            (n-2*k)/2
ans=sigma C(n,2*k)* sigma C(n-2*k,2*m)*2^(n-2*k-2*m)
    k=0             m=0
    n/2
   =sigma C(n,2*k)*2^(n-2*k)*1/2*[(1/2)^(n-2*k)+(3/2)^(n-2*k)]
    k=0
        n/2
   =1/2*sigma C(n,2*k)*[1+3^(n-2*k)] 
        k=0
        n/2                    n/2 
   =1/2*sigma C(n,2*k)+1/2*3^n*sigma C(n,2*k)*3^(-2*k)
        k=0                    k=0
   =2^(n-1)+4*(n-1)
其中化简用到二项式展开

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感谢及赞 (447) longpo 2009-05-19 05:22:32

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