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

Terms

a(0) =1a(1) =0a(2) =0a(3) =2a(4) =6a(5) =0a(6) =4a(7) =48a(8) =36a(9) =8a(10) =216a(11) =648a(12) =232a(13) =768a(14) =5184a(15) =6944a(16) =3696a(17) =28800a(18) =86464a(19) =71712a(20) =137376a(21) =691328a(22) =1185216a(23) =1067904a(24) =4280512a(25) =12749952a(26) =15523200a(27) =26248832a(28) =102010752a(29) =201056256