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

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =3a(5) =0a(6) =6a(7) =24a(8) =6a(9) =10a(10) =90a(11) =90a(12) =25a(13) =240a(14) =540a(15) =261a(16) =540a(17) =2100a(18) =2128a(19) =1533a(20) =6321a(21) =11236a(22) =8064a(23) =16884a(24) =44173a(25) =46980a(26) =51156a(27) =142939a(28) =224991a(29) =212400