a(n) = a(n-1) + Sum_{k=0..floor(log_2(n-1))} a(2^k), a(1) = 1.

Terms

a(0) =1a(1) =2a(2) =5a(3) =8a(4) =19a(5) =30a(6) =41a(7) =52a(8) =115a(9) =178a(10) =241a(11) =304a(12) =367a(13) =430a(14) =493a(15) =556a(16) =1175a(17) =1794a(18) =2413a(19) =3032a(20) =3651a(21) =4270a(22) =4889a(23) =5508a(24) =6127a(25) =6746a(26) =7365a(27) =7984a(28) =8603a(29) =9222