a(n) = ((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).

Terms

a(0) =2a(1) =3a(2) =8a(3) =27a(4) =98a(5) =363a(6) =1352a(7) =5043a(8) =18818a(9) =70227a(10) =262088a(11) =978123a(12) =3650402a(13) =13623483a(14) =50843528a(15) =189750627a(16) =708158978a(17) =2642885283a(18) =9863382152a(19) =36810643323a(20) =137379191138a(21) =512706121227