a(n) = 2*Farey(Fibonacci(n + 1)) - 3.

Terms

a(0) =1a(1) =3a(2) =7a(3) =19a(4) =43a(5) =115a(6) =279a(7) =719a(8) =1879a(9) =4911a(10) =12659a(11) =33235a(12) =86715a(13) =226315a(14) =592767a(15) =1551791a(16) =4060203a(17) =10630767a(18) =27825227a(19) =72843667a(20) =190710291a(21) =499271047a(22) =1307051711a(23) =3421933647a(24) =8958716547a(25) =23453948495a(26) =61403187051a(27) =160755514791a(28) =420862602279