a(n) = (Fibonacci(2*n)-(-1)^n*Fibonacci(n))/2.

Terms

a(0) =0a(1) =1a(2) =1a(3) =5a(4) =9a(5) =30a(6) =68a(7) =195a(8) =483a(9) =1309a(10) =3355a(11) =8900a(12) =23112a(13) =60813a(14) =158717a(15) =416325a(16) =1088661a(17) =2852242a(18) =7463884a(19) =19546175a(20) =51163695a(21) =133962621a(22) =350695511a(23) =918170280a(24) =2403740304a(25) =6293172025a(26) =16475579353a(27) =43133883845a(28) =112925557953