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

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =3a(5) =3a(6) =3a(7) =4a(8) =5a(9) =7a(10) =9a(11) =12a(12) =15a(13) =18a(14) =22a(15) =27a(16) =34a(17) =43a(18) =55a(19) =70a(20) =88a(21) =110a(22) =137a(23) =171a(24) =214a(25) =269a(26) =339a(27) =427a(28) =537a(29) =674