“A Handbook of Integer Sequences” Fifty Years Later(arxiv.org)

  def f(n):
    return n*n + sum(k*k for k in map(int, str(n)))

  >>> [f(i) for i in range(1, 5)]
  [2, 8, 18, 32]

  >>> import heapq, itertools
  >>> seq = heapq.merge((2**i for i in itertools.count(1, 2)),
              (9*2**i for i in itertools.count(1, 2)))
  >>> list(itertools.islice(seq, 0, 4))
  [2, 8, 18, 32]

  import itertools

  def sigma(n):
    return sum(i for i in range(1, n//2+1) if n % i == 0)

  def seq():
    for n in itertools.count(1):
      if sigma(2*n) % 2 == 0: continue
      if sigma(3*n) % 3 == 0: yield n
      continue

  >>> list(itertools.islice(seq(), 0, 4))
  [2, 8, 18, 32]

  def mult(a, b):
    if a == 0 or b == 0: return 0
    if a == 1: return b
    return mult(a-1, b) + b

  >>> mult(5, 9)
  45

  F(0) = 0
  F(n) = 1 + F(n-1)

  F(n) = ((1+sqrt(5))^n - (1-sqrt(5))^n)/(2^n*sqrt(5))