from __future__ import print_function
from math import exp

N = 60

x0 = 5
x1 = 9.0/2

xpp = x0
xp = x1

f = lambda n: 4 + (1.0/2)**n

for n in range(2, N):
    x = -1.0 + 2*xp - (3/4.0)*xpp
    print('n: %4d, sim: %23.23f, formula: %23.23f,  error: %10e' % (n, x, f(n), abs(x-f(n))))
    xpp = xp
    xp = x