_MIN_SUM     = 100
_MAX_SUM     = 200
_MIN_NUM     = 1
_MAX_NUM     = 49
_NUM_CHOICES = 6

def f(n=_NUM_CHOICES, l=_MIN_NUM, s=0, cache={}):
    # Base case.
    if n == 0: return int(_MIN_SUM <= s <= _MAX_SUM)

    key = (n, l, s)
    result = cache.get(key)
    if result is None:
        # Induction.
        result = sum(f(n-1, l=i+1, s=s+i) for i in xrange(l, _MAX_NUM+1))
        cache[key] = result
    return result

if __name__ == '__main__':
    print(f())