a(n) = floor((-1 + 4^n)/(-1 + 2*n)).

Terms

a(0) =3a(1) =5a(2) =12a(3) =36a(4) =113a(5) =372a(6) =1260a(7) =4369a(8) =15420a(9) =55188a(10) =199728a(11) =729444a(12) =2684354a(13) =9942053a(14) =37025580a(15) =138547332a(16) =520602096a(17) =1963413621a(18) =7429132620a(19) =28192605840a(20) =107269427100a(21) =409120605684