Number of binary strings of length n with no substrings equal to 00000 or 00100.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =16a(5) =30a(6) =57a(7) =108a(8) =207a(9) =397a(10) =761a(11) =1456a(12) =2784a(13) =5324a(14) =10185a(15) =19488a(16) =37288a(17) =71341a(18) =136486a(19) =261117a(20) =499561a(21) =955756a(22) =1828549a(23) =3498364a(24) =6693021a(25) =12804983a(26) =24498304a(27) =46869822a(28) =89670729a(29) =171556853