# https://projecteuler.net/problem=65

 import math

# Euler 65
# returns numerator, denominator
def recE(n, j, k):
    if n == 1:
        k = math.ceil(j/3)
        if j % 3 == 2:
            return [1, 2 * k]
        else:
            return [1, 1]
    else:
        r = recE(n - 1, j + 1, k)
        if j % 3 == 2:
            k = math.ceil(j / 3)
            return [r[1], 2 * k * r[1] + r[0]]
        else:
            return [r[1], r[1] + r[0]]
        j -= 1


for a in range(1, 11):
    b = recE(a, 1, 1)
    print(a, "\t", b, "\t", 2 * b[1] + b[0], "/", b[1], "\t", (2 * b[1] + b[0]) / b[1])