递推式:

  • \(f_i=1 (1\leq i\leq 2)\)
  • \(f_i=f_{i-1}+f_{i-2}(i>2)\)

一些性质

  1. \(\sum_{i=1}^n f_i=f_{n+2}-1\)
  2. \(\sum_{i=1}^n f_i^2=f_nf_{n+1}\)
  3. \(\sum_{i=1|i\&1}^{2n-1}=f_{2n}\)
  4. \(\sum_{i=2|!(i\&1)}^{2n}=f_{2n+1}-1\)
  5. \(f_{n+m}=f_{n}f_{m+1}+f_{m}f_{n-1}\)
  6. \(f_{n-1}f_{n+1}=f_{n}^2+(-1)^n\)
  7. \(gcd(f_n, f_m)=f_{gcd(n,m)}\)
05-28 14:58