a(n) = ((1+sqrt(8))*(2+sqrt(2))^n + (1-sqrt(8))*(2-sqrt(2))^n)/2.

Terms

a(0) =1a(1) =6a(2) =22a(3) =76a(4) =260a(5) =888a(6) =3032a(7) =10352a(8) =35344a(9) =120672a(10) =412000a(11) =1406656a(12) =4802624a(13) =16397184a(14) =55983488a(15) =191139584a(16) =652591360a(17) =2228086272a(18) =7607162368a(19) =25972476928a(20) =88675582976a(21) =302757378048