a(n) = (L(n) + L(2*n))/2, where L = A000032 (the Lucas sequence).

Terms

a(0) =2a(1) =2a(2) =5a(3) =11a(4) =27a(5) =67a(6) =170a(7) =436a(8) =1127a(9) =2927a(10) =7625a(11) =19901a(12) =52002a(13) =135982a(14) =355745a(15) =930931a(16) =2436527a(17) =6377807a(18) =16695530a(19) =43706576a(20) =114420627a(21) =299549527a(22) =784218605a(23) =2053091161a(24) =5375030402a(25) =14071960442a(26) =36840786845a(27) =96450296411a(28) =252509934627a(29) =661079236027