a(n) = ceiling((3-sqrt(3))*4^(n-3)) + 1 for n>=2, a(1)=1.

Terms

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