A132583 a(n) = n 2's sandwiched between two 1's.

11, 121, 1221, 12221, 122221, 1222221, 12222221, 122222221, 1222222221, 12222222221, 122222222221, 1222222222221, 12222222222221, 122222222222221, 1222222222222221, 12222222222222221, 122222222222222221, 1222222222222222221, 12222222222222222221, 122222222222222222221

Offset

0,1

Comments

Also, positive numbers each of whose digits indicates its number of adjacent digits (digits on the ends are adjacent to only one while others are adjacent to 2). - Eric Fox, Jul 19 2022

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

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

Formula

a(0) = 11; a(n) = 10*a(n-1) + 11. - Jonathan Vos Post, Nov 24 2007 [corrected by Jon E. Schoenfield, Jan 28 2018]

O.g.f.: 11/((-1+x)*(-1+10*x)) = -(110/9)/(-1+10*x) + (11/9)/(-1+x). - R. J. Mathar, Nov 28 2007

a(n) = 20*(10^n-1)/9 + 10^(n+1) + 1, with n >= 0. - Paolo P. Lava, Dec 19 2007

E.g.f.: 11*exp(x)*(10*exp(9*x) - 1)/9. - Stefano Spezia, Sep 15 2023

Maple

g:=(1+z)/((1-z)*(1-10*z)): gser:=series(g, z=0, 43): seq((coeff(gser, z, n))-1, n=1..24); # Zerinvary Lajos, Feb 25 2009

Mathematica

NestList[10#+11&, 11, 20] (* or *) LinearRecurrence[{11, -10}, {11, 121}, 20] (* Harvey P. Dale, Sep 24 2012 *)

Prog

(Magma) [20*(10^n-1)/9+10^(n+1)+1: n in [0..25]]; // Vincenzo Librandi, Aug 10 2011

Crossrefs

Sequence in context: A106473 A125315 A223676 * A007907 A171285 A216132

Adjacent sequences: A132580 A132581 A132582 * A132584 A132585 A132586

Keyword

nonn,base,easy,changed

Author

Paul Curtz, Nov 21 2007

Status

approved