A253213 a(n) = 10^n + 9.

10, 19, 109, 1009, 10009, 100009, 1000009, 10000009, 100000009, 1000000009, 10000000009, 100000000009, 1000000000009, 10000000000009, 100000000000009, 1000000000000009, 10000000000000009, 100000000000000009, 1000000000000000009, 10000000000000000009, 100000000000000000009

Offset

0,1

Links

Table of n, a(n) for n=0..20.

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

Formula

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

G.f.: (10 - 91*x)/((1 - x)*(1 - 10*x)).

E.g.f.: exp(x)*(exp(9*x) + 9). - Elmo R. Oliveira, Sep 15 2024

Mathematica

Table[10^n + 9, {n, 0, 40}]
LinearRecurrence[{11, -10}, {10, 19}, 40] (* Harvey P. Dale, Jun 29 2018 *)

Prog

(Magma) [10^n+9: n in [0..30]];

Crossrefs

Cf. similar sequences listed in A253208.

Cf. A170955.

Sequence in context: A070199 A015445 A220005 * A293929 A177203 A177167

Adjacent sequences: A253210 A253211 A253212 * A253214 A253215 A253216

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 30 2014

Extensions

a(20) from Elmo R. Oliveira, Sep 15 2024

a(20) corrected by Sean A. Irvine, Sep 22 2024

Status

approved