Let A(n) = floor((3/2)^n), B(n)=3^n-2^n*A(n); then a(n)=2^n-A(n)-B(n)-2.

Terms

a(0) =-2a(1) =-2a(2) =-1a(3) =0a(4) =8a(5) =4a(6) =26a(7) =98a(8) =68a(9) =245a(10) =284a(11) =941a(12) =908a(13) =2921a(14) =866a(15) =3038a(16) =9773a(17) =95842a(18) =26864a(19) =82811a(20) =776048a(21) =235984a(22) =715436a(23) =2157533a(24) =14878043a(25) =27882168a(26) =16575521a(27) =116892244a(28) =82326503a(29) =515542801