a(n) = Sum_{k=0..floor(n/3)} C(n-2k,k-1).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =3a(7) =4a(8) =5a(9) =9a(10) =13a(11) =18a(12) =28a(13) =41a(14) =59a(15) =88a(16) =129a(17) =188a(18) =277a(19) =406a(20) =594a(21) =872a(22) =1278a(23) =1872a(24) =2745a(25) =4023a(26) =5895a(27) =8641a(28) =12664a(29) =18559