a(n) = Sum_{i=0..2} binomial(Fibonacci(n),i).

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =7a(5) =16a(6) =37a(7) =92a(8) =232a(9) =596a(10) =1541a(11) =4006a(12) =10441a(13) =27262a(14) =71254a(15) =186356a(16) =487579a(17) =1276004a(18) =3339821a(19) =8742472a(20) =22885996a(21) =59912932a(22) =156848617a(23) =410626154a(24) =1075018897a(25) =2814412826a(26) =7368190922a(27) =19290113572a(28) =50502074767a(29) =132215989336