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

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =11a(5) =16a(6) =42a(7) =64a(8) =163a(9) =256a(10) =638a(11) =1024a(12) =2510a(13) =4096a(14) =9908a(15) =16384a(16) =39203a(17) =65536a(18) =155382a(19) =262144a(20) =616666a(21) =1048576a(22) =2449868a(23) =4194304a(24) =9740686a(25) =16777216a(26) =38754732a(27) =67108864a(28) =154276028a(29) =268435456