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%I #52 Mar 15 2024 02:19:09
%S 11,121,1221,12221,122221,1222221,12222221,122222221,1222222221,
%T 12222222221,122222222221,1222222222221,12222222222221,
%U 122222222222221,1222222222222221,12222222222222221,122222222222222221,1222222222222222221,12222222222222222221,122222222222222222221
%N a(n) = n 2's sandwiched between two 1's.
%C 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
%H Vincenzo Librandi, <a href="/A132583/b132583.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F a(0) = 11; a(n) = 10*a(n-1) + 11. - _Jonathan Vos Post_, Nov 24 2007 [corrected by _Jon E. Schoenfield_, Jan 28 2018]
%F O.g.f.: 11/((-1+x)*(-1+10*x)) = -(110/9)/(-1+10*x) + (11/9)/(-1+x). - _R. J. Mathar_, Nov 28 2007
%F E.g.f.: 11*exp(x)*(10*exp(9*x) - 1)/9. - _Stefano Spezia_, Sep 15 2023
%p 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
%t NestList[10#+11&,11,20] (* or *) LinearRecurrence[{11,-10},{11,121},20] (* _Harvey P. Dale_, Sep 24 2012 *)
%o (Magma) [20*(10^n-1)/9+10^(n+1)+1: n in [0..25]]; // _Vincenzo Librandi_, Aug 10 2011
%K nonn,base,easy
%O 0,1
%A _Paul Curtz_, Nov 21 2007
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