import math

N = 100  # fill in number of iterations
G = 25  # fill in gcd(a,b)


def binom(x, y):
    if y == x:
        return 1
    if y == 1:
        return x
    if y > x:
        return 0

    a = math.factorial(x)
    b = math.factorial(y)
    c = math.factorial(x-y)
    return a // (b*c)


def nextterm(a, gv):
    b = 0
    if a % 2 == 0:  # even case
        for n in range(a//2 + 1):
            b += ((-1)**(n + (a // 2)) *
                  binom(a//2 + n, a//2 - n) * gv**(4*n))
    else:  # odd case
        for n in range((a-1)//2 + 1):
            b += ((-1)**(n + (a-1)//2) *
                  binom((a-1)//2 + n+1, (a-1)//2 - n) * gv**(2 + 4*n))
    return b


def quotient(a, b):
    return (a**2 + b**2) // (a*b + 1)


for n in range(1, N+1):
    u = nextterm(n, G)
    v = nextterm(n-1, G)
    g = G
    j = (((math.sqrt(g**4 - 4) + g**2) / 2)**n *
         (g / (math.sqrt(g**4 - 4))) -
         (((-1 * (math.sqrt(g**4 - 4))) + g**2) / 2)**n *
         (g / (math.sqrt(g**4 - 4))))

    print("------------- iteration %s -------------" % n)
    print("a_%d = %d" % (n-1, G*v))
    print("a_%d = %d" % (n, G*u))
    print("a*_%d = %d" % (n-1, j))
    print("k = %d" % quotient(G*u, G*v))