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

Author

Paul Curtz, Nov 21 2007

Keywords

• nonn
• base
• easy

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).

Programs

Magma

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

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 *)

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

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