a(n) = ((3+sqrt(2))*(2+sqrt(2))^n + (3-sqrt(2))*(2-sqrt(2))^n)/2.

Terms

a(0) =3a(1) =8a(2) =26a(3) =88a(4) =300a(5) =1024a(6) =3496a(7) =11936a(8) =40752a(9) =139136a(10) =475040a(11) =1621888a(12) =5537472a(13) =18906112a(14) =64549504a(15) =220385792a(16) =752444160a(17) =2569005056a(18) =8771131904a(19) =29946517504a(20) =102243806208a(21) =349082189824