a(n) = Fibonacci(2*n+1) + Fibonacci(2*n-1) + 2.

Terms

a(0) =4a(1) =5a(2) =9a(3) =20a(4) =49a(5) =125a(6) =324a(7) =845a(8) =2209a(9) =5780a(10) =15129a(11) =39605a(12) =103684a(13) =271445a(14) =710649a(15) =1860500a(16) =4870849a(17) =12752045a(18) =33385284a(19) =87403805a(20) =228826129a(21) =599074580a(22) =1568397609a(23) =4106118245a(24) =10749957124a(25) =28143753125a(26) =73681302249a(27) =192900153620