a(n) = (4*10^n + 41)/9.

Terms

a(0) =5a(1) =9a(2) =49a(3) =449a(4) =4449a(5) =44449a(6) =444449a(7) =4444449a(8) =44444449a(9) =444444449a(10) =4444444449a(11) =44444444449a(12) =444444444449