a(n) = 2^n*Lucas(n), where Lucas = A000032.

Terms

a(0) =2a(1) =2a(2) =12a(3) =32a(4) =112a(5) =352a(6) =1152a(7) =3712a(8) =12032a(9) =38912a(10) =125952a(11) =407552a(12) =1318912a(13) =4268032a(14) =13811712a(15) =44695552a(16) =144637952a(17) =468058112a(18) =1514668032a(19) =4901568512a(20) =15861809152a(21) =51329892352a(22) =166107021312a(23) =537533612032