a(0)=3; thereafter, a(n) = A002426(n+1) + Fibonacci(n-1)*(Fibonacci(n-1) + 1).

Terms

a(0) =3a(1) =3a(2) =9a(3) =21a(4) =57a(5) =153a(6) =423a(7) =1179a(8) =3321a(9) =9415a(10) =26843a(11) =76869a(12) =220951a(13) =637107a(14) =1842129a(15) =5339133a(16) =15507641a(17) =45127965a(18) =131548859a(19) =384059009a(20) =1122835671a(21) =3286907517a(22) =9633053985a(23) =28262033613a(24) =82998088607a(25) =243963263943a(26) =717698981853