Number of binary strings of length n with no substrings equal to 0000 or 0010.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =25a(6) =45a(7) =82a(8) =149a(9) =270a(10) =489a(11) =886a(12) =1606a(13) =2911a(14) =5276a(15) =9562a(16) =17330a(17) =31409a(18) =56926a(19) =103173a(20) =186991a(21) =338903a(22) =614229a(23) =1113231a(24) =2017624a(25) =3656749a(26) =6627505a(27) =12011714a(28) =21770074a(29) =39456161