A164139 Number of binary strings of length n with equal numbers of 000 and 011 substrings

1, 2, 4, 6, 9, 14, 22, 38, 66, 120, 222, 416, 792, 1512, 2909, 5610, 10851, 21042, 40864, 79514, 154911, 302210, 590251, 1154012, 2258488, 4423856, 8672541, 17014530, 33404100, 65624480, 129002143, 253733246, 499333096, 983154996, 1936685718