a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-5*k,3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =11a(6) =36a(7) =85a(8) =167a(9) =315a(10) =666a(11) =1605a(12) =3974a(13) =9394a(14) =21051a(15) =46066a(16) =101850a(17) =230720a(18) =530476a(19) =1217951a(20) =2769267a(21) =6247570a(22) =14077081a(23) =31830492a(24) =72252193a(25) =164222206a(26) =372849637a(27) =845040005a(28) =1913511381a(29) =4333973765