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

Terms

a(0) =1a(1) =2a(2) =5a(3) =10a(4) =21a(5) =41a(6) =83a(7) =162a(8) =325a(9) =637a(10) =1275a(11) =2509a(12) =5019a(13) =9907a(14) =19815a(15) =39202a(16) =78405a(17) =155381a(18) =310763a(19) =616665a(20) =1233331a(21) =2449867a(22) =4899735a(23) =9740685a(24) =19481371a(25) =38754731a(26) =77509463a(27) =154276027a(28) =308552055a(29) =614429671