a(n) = (2 + sqrt(2))^n + (2 - sqrt(2))^n.

Terms

a(0) =2a(1) =4a(2) =12a(3) =40a(4) =136a(5) =464a(6) =1584a(7) =5408a(8) =18464a(9) =63040a(10) =215232a(11) =734848a(12) =2508928a(13) =8566016a(14) =29246208a(15) =99852800a(16) =340918784a(17) =1163969536a(18) =3974040576a(19) =13568223232a(20) =46324811776a(21) =158162800640a(22) =540001579008