a(n)=Sum{a(k): k=0,1,2,...,n-3,n-1}; a(n-2) is not a summand; 2 initial terms required.

Terms

a(0) =1a(1) =3a(2) =3a(3) =4a(4) =8a(5) =15a(6) =26a(7) =45a(8) =79a(9) =139a(10) =244a(11) =428a(12) =751a(13) =1318a(14) =2313a(15) =4059a(16) =7123a(17) =12500a(18) =21936a(19) =38495a(20) =67554a(21) =118549a(22) =208039a(23) =365083a(24) =640676a(25) =1124308a(26) =1973023a(27) =3462414a(28) =6076113a(29) =10662835