a(n) = 2*Fibonacci(2*n+2).

Terms

a(0) =2a(1) =6a(2) =16a(3) =42a(4) =110a(5) =288a(6) =754a(7) =1974a(8) =5168a(9) =13530a(10) =35422a(11) =92736a(12) =242786a(13) =635622a(14) =1664080a(15) =4356618a(16) =11405774a(17) =29860704a(18) =78176338a(19) =204668310a(20) =535828592a(21) =1402817466a(22) =3672623806a(23) =9615053952a(24) =25172538050a(25) =65902560198a(26) =172535142544