Moebius inversion of a sequence related to powers of 2.

Terms

a(0) =1a(1) =-1a(2) =-1a(3) =1a(4) =2a(5) =-3a(6) =-5a(7) =9a(8) =15a(9) =-27a(10) =-49a(11) =89a(12) =164a(13) =-304a(14) =-565a(15) =1057a(16) =1987a(17) =-3745a(18) =-7085a(19) =13445a(20) =25575a(21) =-48771a(22) =-93210a(23) =178481a(24) =342392a(25) =-657935a(26) =-1266205a(27) =2440323a(28) =4709403a(29) =-9099507