Upper (1/2)-midsequence of F(n) and F(n+4), where F = A000045 (Fibonacci numbers); see Comments.

Terms

a(0) =2a(1) =3a(2) =5a(3) =8a(4) =12a(5) =20a(6) =32a(7) =51a(8) =83a(9) =134a(10) =216a(11) =350a(12) =566a(13) =915a(14) =1481a(15) =2396a(16) =3876a(17) =6272a(18) =10148a(19) =16419a(20) =26567a(21) =42986a(22) =69552a(23) =112538a(24) =182090a(25) =294627a(26) =476717a(27) =771344a(28) =1248060a(29) =2019404