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 0,1,2.

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =17a(7) =32a(8) =60a(9) =112a(10) =209a(11) =390a(12) =728a(13) =1359a(14) =2537a(15) =4736a(16) =8841a(17) =16504a(18) =30809a(19) =57513a(20) =107363a(21) =200421a(22) =374138a(23) =698426a(24) =1303794a(25) =2433871a(26) =4543454a(27) =8481540a(28) =15833003a(29) =29556423