a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=4.

Terms

a(0) =4a(1) =13a(2) =35a(3) =92a(4) =241a(5) =631a(6) =1652a(7) =4325a(8) =11323a(9) =29644a(10) =77609a(11) =203183a(12) =531940a(13) =1392637a(14) =3645971a(15) =9545276a(16) =24989857a(17) =65424295a(18) =171283028a(19) =448424789a(20) =1173991339a(21) =3073549228a(22) =8046656345a(23) =21066419807a(24) =55152603076a(25) =144391389421a(26) =378021565187a(27) =989673306140