A nonlinear binomial sum.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =15a(5) =27a(6) =47a(7) =80a(8) =134a(9) =222a(10) =365a(11) =597a(12) =973a(13) =1582a(14) =2568a(15) =4164a(16) =6747a(17) =10927a(18) =17691a(19) =28636a(20) =46346a(21) =75002a(22) =121369a(23) =196393a(24) =317785a(25) =514202a(26) =832012a(27) =1346240a(28) =2178279a(29) =3524547