Consider constructing binary words that begin with 0 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).

A340215

Consider constructing binary words that begin with 0 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).