A164188 Number of binary strings of length n with equal numbers of 00000 and 10001 substrings

1, 2, 4, 8, 16, 30, 57, 108, 204, 385, 729, 1381, 2619, 4973, 9452, 17987, 34268, 65361, 124813, 238619, 456731, 875234, 1679169, 3225296, 6202198, 11940392, 23013524, 44405122, 85775159, 165867285, 321086662, 622210063, 1206966882, 2343619235