https://oeis.org/A001105 starts with 0 so I guess you don't mean that obvious quadratic.

Could be https://oeis.org/A209303 :

  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]

but I don't know why that entry doesn't start with 0.

Could be https://oeis.org/A190787 :

  >>> 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]

Or https://oeis.org/A067051:

  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]

The others are either degenerate for 4 points of the A001105 case, or are not so easy to implement in raw Python.