a(n) = A000108(n) + A014137(n).

Terms

a(0) =2a(1) =3a(2) =6a(3) =14a(4) =37a(5) =107a(6) =329a(7) =1055a(8) =3486a(9) =11780a(10) =40510a(11) =141286a(12) =498524a(13) =1776312a(14) =6382292a(15) =23097542a(16) =84118037a(17) =308049947a(18) =1133682557a(19) =4190570237a(20) =15551547887a(21) =57919961507a(22) =216418821767a(23) =811055485427