a(n) = ceiling((9*(9/4)^n - 4) / 5).

Terms

a(0) =1a(1) =4a(2) =9a(3) =20a(4) =46a(5) =103a(6) =233a(7) =525a(8) =1182a(9) =2660a(10) =5985a(11) =13467a(12) =30301a(13) =68178a(14) =153401a(15) =345152a(16) =776591a(17) =1747331a(18) =3931496a(19) =8845866a(20) =19903198a(21) =44782196a(22) =100759940a(23) =226709866a(24) =510097200a(25) =1147718700a(26) =2582367076a(27) =5810325920a(28) =13073233321a(29) =29414774973