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 2,3,4.

Terms

a(0) =2a(1) =3a(2) =4a(3) =7a(4) =13a(5) =25a(6) =47a(7) =88a(8) =164a(9) =306a(10) =571a(11) =1066a(12) =1990a(13) =3715a(14) =6935a(15) =12946a(16) =24167a(17) =45114a(18) =84217a(19) =157213a(20) =293479a(21) =547855a(22) =1022714a(23) =1909162a(24) =3563948a(25) =6653037a(26) =12419626a(27) =23184466a(28) =43279843a(29) =80793097