a(n) = Sum_{k=0..floor(n/4)} (n-3*k+1) * binomial(n-3*k,k)^2.

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =7a(5) =18a(6) =43a(7) =88a(8) =162a(9) =298a(10) =583a(11) =1188a(12) =2402a(13) =4722a(14) =9123a(15) =17648a(16) =34463a(17) =67632a(18) =132382a(19) =257748a(20) =500244a(21) =970790a(22) =1885815a(23) =3663816a(24) =7110990a(25) =13783264a(26) =26692422a(27) =51672484a(28) =100007876a(29) =193487262