a(n) = Sum_{i=1..Fibonacci(n)} sigma_0(i) where sigma_0(n) is A000005(n).

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =10a(5) =20a(6) =37a(7) =70a(8) =127a(9) =231a(10) =413a(11) =746a(12) =1307a(13) =2295a(14) =4010a(15) =6957a(16) =12031a(17) =20712a(18) =35514a(19) =60718a(20) =103500a(21) =175989a(22) =298539a(23) =505399a(24) =853777a(25) =1439856a(26) =2424299a(27) =4075479a(28) =6841787a(29) =11470592