a(n) = Fibonacci(2n-1) - 2^n + binomial(n,2) + 2.

Terms

a(0) =2a(1) =1a(2) =1a(3) =2a(4) =5a(5) =14a(6) =42a(7) =128a(8) =384a(9) =1123a(10) =3204a(11) =8955a(12) =24629a(13) =66913a(14) =180127a(15) =481568a(16) =1280855a(17) =3393644a(18) =8965476a(19) =23633702a(20) =62197602a(21) =163483201a(22) =429300366a(23) =1126514817a(24) =2954438135a(25) =7745187919a(26) =20297902537a(27) =53182073798a(28) =139315427369a(29) =364898425658