a(n) = 2*(10^n - 1)/9.

Terms

a(0) =0a(1) =2a(2) =22a(3) =222a(4) =2222a(5) =22222a(6) =222222a(7) =2222222a(8) =22222222a(9) =222222222a(10) =2222222222a(11) =22222222222a(12) =222222222222