A164187 Number of binary strings of length n with equal numbers of 00000 and 01110 substrings

1, 2, 4, 8, 16, 30, 57, 108, 204, 389, 739, 1407, 2683, 5113, 9764, 18654, 35669, 68287, 130819, 250884, 481590, 925271, 1779499, 3425460, 6600137, 12729083, 24571939, 47477432, 91818595, 177732486, 344344010, 667728900, 1295942046, 2517340377