a(n) = ((1+4*sqrt(2))*(2+sqrt(2))^n + (1-4*sqrt(2))*(2-sqrt(2))^n)/2.

Terms

a(0) =1a(1) =10a(2) =38a(3) =132a(4) =452a(5) =1544a(6) =5272a(7) =18000a(8) =61456a(9) =209824a(10) =716384a(11) =2445888a(12) =8350784a(13) =28511360a(14) =97343872a(15) =332352768a(16) =1134723328a(17) =3874187776a(18) =13227304448a(19) =45160842240a(20) =154188760064a(21) =526433355776