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

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =4a(5) =0a(6) =10a(7) =40a(8) =10a(9) =20a(10) =180a(11) =180a(12) =55a(13) =560a(14) =1260a(15) =616a(16) =1435a(17) =5600a(18) =5684a(19) =4424a(20) =18956a(21) =33720a(22) =24780a(23) =55944a(24) =147249a(25) =157560a(26) =182280a(27) =523540a(28) =826440a(29) =802560