a(n) = (5*4^n + (-2)^n)/6.

Terms

a(0) =1a(1) =3a(2) =14a(3) =52a(4) =216a(5) =848a(6) =3424a(7) =13632a(8) =54656a(9) =218368a(10) =873984a(11) =3494912a(12) =13981696a(13) =55922688a(14) =223698944a(15) =894779392a(16) =3579150336a(17) =14316535808a(18) =57266274304a(19) =229064835072a(20) =916259864576