byun_the_exponental.py

mem = {} #simple memorization
def byun_count(years):
    if years in mem:
        return mem[years]

    count = 1
    life = years
    while life > 0:
        for i in range(2):
            life -= 1
            count += byun_count(life)
            if life == 0:
                break
        life -= 2 # absence
        if life <= 0:
            break

    mem[years] = count
    return count


assert byun_count(0) == 1
assert byun_count(1) == 2
assert byun_count(2) == 4
assert byun_count(3) == 7
assert byun_count(4) == 12 

print(byun_count(100))