a(0) = 0, a(n+1) = 2*a(n) + (-1)^floor(n/3).

Terms

a(0) =0a(1) =1a(2) =3a(3) =7a(4) =13a(5) =25a(6) =49a(7) =99a(8) =199a(9) =399a(10) =797a(11) =1593a(12) =3185a(13) =6371a(14) =12743a(15) =25487a(16) =50973a(17) =101945a(18) =203889a(19) =407779a(20) =815559a(21) =1631119a(22) =3262237a(23) =6524473a(24) =13048945a(25) =26097891a(26) =52195783a(27) =104391567a(28) =208783133a(29) =417566265