a(n) = Sum_{k=0..n} binomial(floor(n-2k/3), k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =16a(7) =28a(8) =48a(9) =81a(10) =136a(11) =229a(12) =388a(13) =661a(14) =1129a(15) =1928a(16) =3287a(17) =5594a(18) =9510a(19) =16164a(20) =27484a(21) =46757a(22) =79577a(23) =135454a(24) =230552a(25) =392355a(26) =667620a(27) =1135924a(28) =1932721a(29) =3288563