Number of binary strings of length n with no substrings equal to 0000 or 0111.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =14a(5) =25a(6) =44a(7) =77a(8) =134a(9) =233a(10) =405a(11) =703a(12) =1220a(13) =2117a(14) =3673a(15) =6372a(16) =11054a(17) =19176a(18) =33265a(19) =57705a(20) =100101a(21) =173645a(22) =301221a(23) =522526a(24) =906422a(25) =1572363a(26) =2727565a(27) =4731484a(28) =8207665a(29) =14237766