a(n) = Sum_{k=0..n} 2^max(k, n-k).

Terms

a(0) =1a(1) =4a(2) =10a(3) =24a(4) =52a(5) =112a(6) =232a(7) =480a(8) =976a(9) =1984a(10) =4000a(11) =8064a(12) =16192a(13) =32512a(14) =65152a(15) =130560a(16) =261376a(17) =523264a(18) =1047040a(19) =2095104a(20) =4191232a(21) =8384512a(22) =16771072a(23) =33546240a(24) =67096576a(25) =134201344a(26) =268410880a(27) =536838144a(28) =1073692672a(29) =2147418112