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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =16a(5) =50a(6) =135a(7) =413a(8) =1456a(9) =5160a(10) =17490a(11) =58245a(12) =196471a(13) =673244a(14) =2316769a(15) =7955948a(16) =27305840a(17) =93934384a(18) =324040536a(19) =1119701787a(20) =3872489826a(21) =13404527930a(22) =46448444889a(23) =161120715822a(24) =559403953207