cp's OEIS Frontend

Python

from itertools import product
def is_prefix_normal(w):
  for k in range(1, len(w)+1):
    weight0 = w[:k].count("1")
    for j in range(1, len(w)-k+1):
      weightj = w[j:j+k].count("1")
      if weightj > weight0: return False
  return True
def bin_pals(digits):
  midrange = [[""], ["0", "1"]]
  for p in product("01", repeat=digits//2):
    left = "".join(p)
    for middle in midrange[digits%2]:
      yield left+middle+left[::-1]
def a(n):
  return sum(is_prefix_normal(w) for w in bin_pals(n))
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Dec 19 2020