Sum of terms of A293630 after generating the sequence for n steps (see comments).

Terms

a(0) =3a(1) =5a(2) =9a(3) =17a(4) =47a(5) =93a(6) =185a(7) =369a(8) =1103a(9) =2205a(10) =4409a(11) =13223a(12) =26445a(13) =52889a(14) =105777a(15) =317327a(16) =634653a(17) =1269305a(18) =2538609a(19) =5077217a(20) =15231647a(21) =30463293a(22) =60926585a(23) =182779751a(24) =365559501a(25) =731119001a(26) =1462238001a(27) =4386713999a(28) =8773427997a(29) =26320283987