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

Terms

a(0) =1a(1) =0a(2) =0a(3) =4a(4) =0a(5) =0a(6) =12a(7) =36a(8) =0a(9) =32a(10) =288a(11) =0a(12) =80a(13) =1440a(14) =720a(15) =192a(16) =5760a(17) =8640a(18) =448a(19) =20160a(20) =60480a(21) =13120a(22) =64512a(23) =322560a(24) =195840a(25) =193536a(26) =1451520a(27) =1746944a(28) =739584a(29) =5806080