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

Terms

a(0) =1a(1) =2a(2) =5a(3) =10a(4) =23a(5) =46a(6) =102a(7) =204a(8) =443a(9) =886a(10) =1898a(11) =3796a(12) =8054a(13) =16108a(14) =33932a(15) =67864a(16) =142163a(17) =284326a(18) =592962a(19) =1185924a(20) =2464226a(21) =4928452a(22) =10209620a(23) =20419240a(24) =42190558a(25) =84381116a(26) =173962532a(27) =347925064a(28) =715908428a(29) =1431816856