a(n) = Sum_{k=0..n} (1-(-1)^( floor( (-n-k)/2^k ) )) * 2^(k-1).

Terms

a(0) =0a(1) =3a(2) =4a(3) =9a(4) =26a(5) =59a(6) =112a(7) =245a(8) =502a(9) =1015a(10) =2036a(11) =4081a(12) =8178a(13) =16355a(14) =32744a(15) =65517a(16) =131054a(17) =262127a(18) =524268a(19) =1048553a(20) =2097130a(21) =4194283a(22) =8388576a(23) =16777189a(24) =33554406a(25) =67108839a(26) =134217700a(27) =268435425a(28) =536870850a(29) =1073741779