a(n) = Sum{a(k): k=0,1,2,...,n-4,n-2,n-1}; a(n-3) is not a summand; initial terms are 1,2,2.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =7a(5) =14a(6) =26a(7) =49a(8) =91a(9) =170a(10) =317a(11) =592a(12) =1105a(13) =2063a(14) =3851a(15) =7189a(16) =13420a(17) =25052a(18) =46766a(19) =87301a(20) =162970a(21) =304226a(22) =567917a(23) =1060165a(24) =1979074a(25) =3694457a(26) =6896666a(27) =12874423a(28) =24033463a(29) =44864717