x <- c(1618,1674,1728,1753,1775,1785,1797,1815)
n<-length(x)
x1<-numeric(n);
for(i in 1:n)   ##一次累加
{
  x1[i]<-sum(x[1:i]);
}
z = diff(x1) #
m = n-3
v_m = c()
for(i in 1:m){
  y=c()
  for(j in 1:(n-i-1)){
    y = c(y,z[j+i]-z[j])
  }
  for(k in 1:(n-i-2)){
    v_m = c(v_m,log(y[k+1]/y[k]))
  }
}
v = sum(v_m)/length(v_m)
v
A = matrix(c(exp(seq(1,n)*v),seq(1,n),rep(1,n)),nrow = n, ncol = 3)
c<-solve(t(A)%*%A)%*%t(A)%*%x1;
c

# 拟合
x_1 = c()
for(i in 1:n){
  x_1 = c(x_1,c[1]*exp(v*i)+c[2]*i+c[3])
}
x_0 = c(x_1[1],diff(x_1))
x_0