a(n) = floor((-1 + 4^n)/(-1 + 4*n)).

Terms

a(0) =1a(1) =2a(2) =5a(3) =17a(4) =53a(5) =178a(6) =606a(7) =2114a(8) =7489a(9) =26886a(10) =97541a(11) =356962a(12) =1315860a(13) =4880644a(14) =18199013a(15) =68174084a(16) =256415957a(17) =967879954a(18) =3665038759a(19) =13917868706a(20) =52988512181a(21) =202209034993a(22) =773282903051