a(n) = ceiling((3-sqrt(3))*4^(n-3)) + 1.

Terms

a(0) =2a(1) =2a(2) =2a(3) =3a(4) =7a(5) =22a(6) =83a(7) =326a(8) =1300a(9) =5195a(10) =20776a(11) =83098a(12) =332387a(13) =1329543a(14) =5318166a(15) =21272659a(16) =85090631a(17) =340362521a(18) =1361450080a(19) =5445800316a(20) =21783201259a(21) =87132805033a(22) =348531220128