a(n) = Sum_{k=0..n} (k+1) * binomial(k,3*(n-k)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =9a(5) =26a(6) =67a(7) =148a(8) =296a(9) =570a(10) =1103a(11) =2172a(12) =4313a(13) =8528a(14) =16691a(15) =32360a(16) =62365a(17) =119830a(18) =229840a(19) =440052a(20) =840653a(21) =1602038a(22) =3045967a(23) =5779676a(24) =10947997a(25) =20706438a(26) =39107943a(27) =73764072a(28) =138955192a(29) =261449646