a(0) = 1, a(n) + a(n+1) = round(2^n/9), n >= 0.

Terms

a(0) =1a(1) =-1a(2) =1a(3) =-1a(4) =2a(5) =0a(6) =4a(7) =3a(8) =11a(9) =17a(10) =40a(11) =74a(12) =154a(13) =301a(14) =609a(15) =1211a(16) =2430a(17) =4852a(18) =9712a(19) =19415a(20) =38839a(21) =77669a(22) =155348a(23) =310686a(24) =621382a(25) =1242753a(26) =2485517a(27) =4971023a(28) =9942058a(29) =19884104