a(n) = (4^n - 2^n)/2 + 3^n.

Terms

a(0) =1a(1) =4a(2) =15a(3) =55a(4) =201a(5) =739a(6) =2745a(7) =10315a(8) =39201a(9) =150499a(10) =582825a(11) =2273275a(12) =8918001a(13) =35144659a(14) =138992505a(15) =551203435a(16) =2190497601a(17) =8719009219a(18) =34747027785a(19) =138600952795a(20) =553242074001