A199691 a(n) = 11*10^n + 1.

12, 111, 1101, 11001, 110001, 1100001, 11000001, 110000001, 1100000001, 11000000001, 110000000001, 1100000000001, 11000000000001, 110000000000001, 1100000000000001, 11000000000000001, 110000000000000001, 1100000000000000001, 11000000000000000001, 110000000000000000001

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = 10*a(n-1) - 9.

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

G.f.: 3*(4-7*x)/((1-x)*(1-10*x)).

From Elmo R. Oliveira, Jun 10 2025: (Start)

E.g.f.: exp(x)*(1 + 11*exp(9*x)).

a(n) = 3*A199690(n). (End)

Mathematica

11 10^Range[0, 20]+1 (* Harvey P. Dale, Jan 29 2023 *)
(* Alternative: *)
LinearRecurrence[{11, -10}, {12, 111}, 20] (* Harvey P. Dale, Jan 29 2023 *)

Prog

(Magma) [11*10^n+1: n in [0..30]];

Crossrefs

Cf. A199690.

Sequence in context: A036733 A253091 A123933 * A348150 A077754 A199357

Adjacent sequences: A199688 A199689 A199690 * A199692 A199693 A199694

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Nov 09 2011

Status

approved