def euler_65():
"""Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e."""
from eutil import nth, digits
def sequence():
num = []
t = 0
while True:
if t == 0:
num.append(1)
elif t == 1:
num.append(2)
else:
coef = t / 3 * 2 if t % 3 == 0 else 1
num.append(coef * num[t - 1] + num[t - 2])
yield num[-1]
t += 1
return sum(digits(nth(sequence(), 100)))
def multinomial(n):
alphabet = dict([(d, digits(n).count(d)) for d in set(digits(n))])
alphabet[0] = 7 - len(str(n))
return factorial(sum(alphabet.values())) / reduce(mul, map(factorial, alphabet.values()))
def sum_sq_digits(n):
return sum([x ** 2 for x in digits(n)])
