a(n) = 4*a(n-1) - a(n-2) - 2, with a(0)=1, a(1)=2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =57a(5) =210a(6) =781a(7) =2912a(8) =10865a(9) =40546a(10) =151317a(11) =564720a(12) =2107561a(13) =7865522a(14) =29354525a(15) =109552576a(16) =408855777a(17) =1525870530a(18) =5694626341a(19) =21252634832a(20) =79315912985a(21) =296011017106