Fibonacci-accumulation sequence.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =4a(6) =3a(7) =7a(8) =5a(9) =12a(10) =8a(11) =20a(12) =13a(13) =33a(14) =21a(15) =54a(16) =34a(17) =88a(18) =55a(19) =143a(20) =89a(21) =232a(22) =144a(23) =376a(24) =233a(25) =609a(26) =377a(27) =986a(28) =610a(29) =1596