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 0,3,4.

Terms

a(0) =0a(1) =3a(2) =4a(3) =7a(4) =11a(5) =21a(6) =39a(7) =74a(8) =138a(9) =258a(10) =481a(11) =898a(12) =1676a(13) =3129a(14) =5841a(15) =10904a(16) =20355a(17) =37998a(18) =70933a(19) =132415a(20) =247187a(21) =461439a(22) =861396a(23) =1608020a(24) =3001788a(25) =5603619a(26) =10460614a(27) =19527460a(28) =36453089a(29) =68049183