Number of binary strings of length n with no substrings equal to 0001 or 0010.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =25a(6) =44a(7) =78a(8) =137a(9) =241a(10) =423a(11) =743a(12) =1304a(13) =2289a(14) =4017a(15) =7050a(16) =12372a(17) =21712a(18) =38102a(19) =66865a(20) =117340a(21) =205918a(22) =361361a(23) =634145a(24) =1112847a(25) =1952911a(26) =3427120a(27) =6014177a(28) =10554145a(29) =18521234