A164144 Number of binary strings of length n with equal numbers of 001 and 101 substrings

1, 2, 4, 6, 8, 11, 18, 36, 76, 153, 289, 525, 954, 1787, 3464, 6832, 13452, 26207, 50603, 97525, 188805, 367994, 720805, 1414179, 2772486, 5428759, 10626469, 20818945, 40850896, 80275617, 157897960, 310707852, 611510788, 1203795095, 2370700373