#!/usr/bin/env python3

from itertools import combinations_with_replacement as comb

bound = 200
sieve = [i-1 for i in range(bound+1)]
dup = []

def rec(chain, sieve, bound, id=0):
    c = 1
    for m in chain:
        n = m+chain[0]
        if n > bound:
            continue
        if len(chain) >= max(sieve[n:n+3]): #<-- trial and error magic
            continue
        if len(chain) < sieve[n]:
            sieve[n] = len(chain)
        c += rec([n] + chain, sieve, bound, id+1)
    return c

rec([1], sieve, bound)
print(sum(sieve[2:]))