a(1)..a(4) = 0,0,0,1; thereafter a(n) = a(n-2)+a(n-3)+2*(d(n-3)+d(n-4)) where d(n) = A238824(n).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =2a(5) =5a(6) =11a(7) =27a(8) =64a(9) =158a(10) =387a(11) =956a(12) =2355a(13) =5809a(14) =14313a(15) =35272a(16) =86894a(17) =214075a(18) =527368a(19) =1299185a(20) =3200551a(21) =7884653a(22) =19424072a(23) =47851896a(24) =117884841a(25) =290413626a(26) =715444487a(27) =1762523473a(28) =4342040215a(29) =10696772780