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

Terms

a(0) =1a(1) =2a(2) =4a(3) =14a(4) =64a(5) =248a(6) =868a(7) =3176a(8) =12352a(9) =48344a(10) =186688a(11) =720896a(12) =2810128a(13) =11021984a(14) =43290688a(15) =170193632a(16) =670576384a(17) =2648370560a(18) =10477291072a(19) =41502538880a(20) =164602863616a(21) =653632824704