a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=3.

Terms

a(0) =3a(1) =10a(2) =27a(3) =71a(4) =186a(5) =487a(6) =1275a(7) =3338a(8) =8739a(9) =22879a(10) =59898a(11) =156815a(12) =410547a(13) =1074826a(14) =2813931a(15) =7366967a(16) =19286970a(17) =50493943a(18) =132194859a(19) =346090634a(20) =906077043a(21) =2372140495a(22) =6210344442a(23) =16258892831a(24) =42566334051a(25) =111440109322a(26) =291753993915a(27) =763821872423