a(n) = floor( (4/5)*( (9/4)^(n+1)-1 ) ).

Terms

a(0) =1a(1) =3a(2) =8a(3) =19a(4) =45a(5) =102a(6) =232a(7) =524a(8) =1181a(9) =2659a(10) =5984a(11) =13466a(12) =30300a(13) =68177a(14) =153400a(15) =345151a(16) =776590a(17) =1747330a(18) =3931495a(19) =8845865a(20) =19903197a(21) =44782195a(22) =100759939a(23) =226709865a(24) =510097199a(25) =1147718699a(26) =2582367075a(27) =5810325919a(28) =13073233320a(29) =29414774972