a(n,m) =Floor[N[(-2 + Sqrt[3])^n + (-2 - Sqrt[3])^n]/2^m].

Terms

a(0) =-2a(1) =7a(2) =3a(3) =-26a(4) =-13a(5) =-7a(6) =96a(7) =48a(8) =24a(9) =12a(10) =-362a(11) =-181a(12) =-91a(13) =-46a(14) =-23a(15) =1350a(16) =675a(17) =337a(18) =168a(19) =84a(20) =42a(21) =-5042a(22) =-2521a(23) =-1261a(24) =-631a(25) =-316a(26) =-158a(27) =-79a(28) =18816a(29) =9408