a(n) = -(u^n-1)*(v^n-1) with u = 1+sqrt(2), v = 1-sqrt(2).

Terms

a(0) =2a(1) =4a(2) =14a(3) =32a(4) =82a(5) =196a(6) =478a(7) =1152a(8) =2786a(9) =6724a(10) =16238a(11) =39200a(12) =94642a(13) =228484a(14) =551614a(15) =1331712a(16) =3215042a(17) =7761796a(18) =18738638a(19) =45239072a(20) =109216786a(21) =263672644a(22) =636562078a(23) =1536796800a(24) =3710155682a(25) =8957108164a(26) =21624372014a(27) =52205852192