A nonlinear binomial sum.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =16a(5) =31a(6) =58a(7) =105a(8) =185a(9) =319a(10) =541a(11) =906a(12) =1503a(13) =2476a(14) =4058a(15) =6626a(16) =10790a(17) =17537a(18) =28464a(19) =46155a(20) =74791a(21) =121137a(22) =196139a(23) =317508a(24) =513901a(25) =831686a(26) =1345888a(27) =2177900a(28) =3524140a(29) =5702419