a(n) = (2*10^n - 11)/9.

Terms

a(0) =1a(1) =21a(2) =221a(3) =2221a(4) =22221a(5) =222221a(6) =2222221a(7) =22222221a(8) =222222221a(9) =2222222221a(10) =22222222221a(11) =222222222221