由 --- 於 星期三 五月 21, 2003 10:05 pm
fn=f[n-1]+f[n-2]+f[n-3]+f[n-4]+f[n-5]
G(x)=f0+f1*x+f2*xx+f3*x^3+....
G(x)*x=f0*x+f1*xx+f2*xxx+f3*x^4+....
G(x)*xx=f0*xx+f1*xxx+f2*xxxx+f3*x^5+....
G(x)*xxx=f0*xxx+f1*xxxx+f2*xxxxx+f3*x^6+....
G(x)*xxxx=f0*xxxx+f1*xxxxx+f2*xxxxxx+f3*x^7+....
-------------------------------------------------------------------
G(x)*(1+x+xx+xxx+xxxx)=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+(f0+f1+f2+f3+f4)xxxx+(f1+f2+f3+f4+f5)xxxxx+...
=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+f5*xxxx+f6*xxxxx+...
=f0+(f0+f1)x+(f0+f1+f2)xx+(f0+f1+f2+f3)xxx+(G(x)-f0-f1x-f2xx-f3xxx-f4xxxx)/x
so, we can get G(x)
G(1/2) is what we want.