a(n) = Sum_{k=0,1,2,...,n-4,n-2,n-1} a(k); a(n-3) is not a summand, with a(0)=a(1)=a(2)=1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =15a(7) =28a(8) =52a(9) =97a(10) =181a(11) =338a(12) =631a(13) =1178a(14) =2199a(15) =4105a(16) =7663a(17) =14305a(18) =26704a(19) =49850a(20) =93058a(21) =173717a(22) =324288a(23) =605368a(24) =1130077a(25) =2109583a(26) =3938086a(27) =7351463a(28) =13723420a(29) =25618337