A173770 a(n) = (4*10^n - 13)/9.

3, 43, 443, 4443, 44443, 444443, 4444443, 44444443, 444444443, 4444444443, 44444444443, 444444444443, 4444444444443, 44444444444443, 444444444444443, 4444444444444443, 44444444444444443, 444444444444444443, 4444444444444444443, 44444444444444444443, 444444444444444444443

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..990

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Formula

a(n) = 10*a(n-1) + 13 (with a(1)=3).

G.f.: x*(3+10*x)/((10*x-1)*(x-1)). - R. J. Mathar, Aug 23 2011

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

E.g.f.: 1 + exp(x)*(4*exp(9*x) - 13)/9.

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

Example

For n=2, a(2)=10*3+13=43; n=3, a(3)=10*43+13=443; n=4, a(4)=10*443+13=4443.

Mathematica

(4*10^Range[25] - 13)/9 (* Paolo Xausa, Jun 27 2025 *)

Prog

(PARI) my(x='x+O('x^22)); Vec(x*(3+10*x)/((1-11*x+10*x^2))) \\ Elmo R. Oliveira, Jun 19 2025

Crossrefs

Cf. A093163.

Sequence in context: A138974 A036940 A099664 * A093163 A199020 A211959

Adjacent sequences: A173767 A173768 A173769 * A173771 A173772 A173773

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 24 2010

Extensions

More terms from Elmo R. Oliveira, Jun 19 2025

Status

approved