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) =2a(1) =3a(2) =3a(3) =5a(4) =10a(5) =18a(6) =31a(7) =54a(8) =95a(9) =167a(10) =293a(11) =514a(12) =902a(13) =1583a(14) =2778a(15) =4875a(16) =8555a(17) =15013a(18) =26346a(19) =46234a(20) =81135a(21) =142382a(22) =249863a(23) =438479a(24) =769477a(25) =1350338a(26) =2369678a(27) =4158495a(28) =7297650a(29) =12806483