A173768 a(n) = (4*10^n - 31)/9.

1, 41, 441, 4441, 44441, 444441, 4444441, 44444441, 444444441, 4444444441, 44444444441, 444444444441, 4444444444441, 44444444444441, 444444444444441, 4444444444444441, 44444444444444441, 444444444444444441, 4444444444444444441, 44444444444444444441, 444444444444444444441

Offset: 1

Author

Vincenzo Librandi, Feb 24 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A093174.

Programs

Magma

[(4*10^n-31)/9: n in [1..20]]; // Vincenzo Librandi, Aug 20 2014

Mathematica

NestList[10#+31&,1,20] (* or *) Table[FromDigits[PadLeft[{1},n,4]],{n,20}] (* Harvey P. Dale, May 28 2013 *)
Table[(4 10^n - 31)/9, {n, 1, 30}] (* Vincenzo Librandi, Aug 20 2014 *)

Formula

a(n) = 10*a(n-1) + 31, n>1.

G.f.: x*(1+30*x)/((10*x-1)*(x-1)).

From Elmo R. Oliveira, Jun 19 2025: (Start)

E.g.f.: 3 + exp(x)*(4*exp(9*x) - 31)/9.

a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)