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

Terms

a(0) =5a(1) =52a(2) =374a(3) =2581a(4) =17708a(5) =121390a(6) =832037a(7) =5702884a(8) =39088166a(9) =267914293a(10) =1836311900a(11) =12586269022a(12) =86267571269a(13) =591286729876