a(n) = floor((2*3^n+3*2^n)/5).

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =42a(5) =116a(6) =330a(7) =951a(8) =2778a(9) =8180a(10) =24234a(11) =72087a(12) =215034a(13) =642644a(14) =1923018a(15) =5759223a(16) =17258010a(17) =51734708a(18) =155125482a(19) =465219159a(20) =1395342906a(21) =4185399572a(22) =12554940426a(23) =37662304695a(24) =112981880922a(25) =338935576436