a(0)=1, a(n) = Fibonacci(2n+4) - (2n+3).

Terms

a(0) =1a(1) =3a(2) =14a(3) =46a(4) =133a(5) =364a(6) =972a(7) =2567a(8) =6746a(9) =17690a(10) =46345a(11) =121368a(12) =317784a(13) =832011a(14) =2178278a(15) =5702854a(16) =14930317a(17) =39088132a(18) =102334116a(19) =267914255a(20) =701408690a(21) =1836311858a(22) =4807526929a(23) =12586268976a(24) =32951280048a(25) =86267571219a(26) =225851433662