a(n) = Sum_{k=0..floor(n/2)} A027157(n-k, k).

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =15a(5) =24a(6) =50a(7) =81a(8) =165a(9) =266a(10) =544a(11) =875a(12) =1787a(13) =2876a(14) =5870a(15) =9445a(16) =19281a(17) =31022a(18) =63324a(19) =101887a(20) =207975a(21) =334624a(22) =683050a(23) =1099001a(24) =2243325a(25) =3609426a(26) =7367704a(27) =11854355a(28) =24197587a(29) =38932996