a(n) = floor((7*2^(n+1)-9*n-10)/3).

Terms

a(0) =1a(1) =3a(2) =9a(3) =25a(4) =59a(5) =131a(6) =277a(7) =573a(8) =1167a(9) =2359a(10) =4745a(11) =9521a(12) =19075a(13) =38187a(14) =76413a(15) =152869a(16) =305783a(17) =611615a(18) =1223281a(19) =2446617a(20) =4893291a(21) =9786643a(22) =19573349a(23) =39146765a(24) =78293599a(25) =156587271a(26) =313174617a(27) =626349313a(28) =1252698707a(29) =2505397499