Number of length-n binary words having exactly one nontrivial palindrome prefix.

Terms

a(0) =0a(1) =2a(2) =4a(3) =10a(4) =18a(5) =34a(6) =62a(7) =118a(8) =222a(9) =432a(10) =834a(11) =1642a(12) =3230a(13) =6406a(14) =12702a(15) =25298a(16) =50386a(17) =100566a(18) =200716a(19) =401022a(20) =801230a(21) =1601654a(22) =3201694a(23) =6401784a(24) =12800378a(25) =25597578a(26) =51188806a(27) =102371284a(28) =204729938a(29) =409447272