a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(k,n-3*k)^2.

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =2a(5) =0a(6) =3a(7) =12a(8) =3a(9) =4a(10) =36a(11) =36a(12) =9a(13) =80a(14) =180a(15) =86a(16) =155a(17) =600a(18) =607a(19) =402a(20) =1581a(21) =2808a(22) =1967a(23) =3780a(24) =9816a(25) =10376a(26) =10584a(27) =28626a(28) =44918a(29) =41184