a(n) = ((5+sqrt(2))*(2+sqrt(2))^n + (5-sqrt(2))*(2-sqrt(2))^n)/2.

Terms

a(0) =5a(1) =12a(2) =38a(3) =128a(4) =436a(5) =1488a(6) =5080a(7) =17344a(8) =59216a(9) =202176a(10) =690272a(11) =2356736a(12) =8046400a(13) =27472128a(14) =93795712a(15) =320238592a(16) =1093362944a(17) =3732974592a(18) =12745172480a(19) =43514740736a(20) =148568617984a(21) =507244990464