A133384 - OEIS

%I #38 Dec 01 2023 03:27:45

%S 12,102,1002,10002,100002,1000002,10000002,100000002,1000000002,

%T 10000000002,100000000002,1000000000002,10000000000002,

%U 100000000000002,1000000000000002,10000000000000002,100000000000000002,1000000000000000002,10000000000000000002

%N Numbers with n 0's between 1 and 2.

%H Vincenzo Librandi, <a href="/A133384/b133384.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 10^(n+1) + 2. - _Vincenzo Librandi_, Aug 10 2011

%F a(n) = 11*a(n-1) - 10*a(n-2); a(0)=12, a(1)=102. - _Harvey P. Dale_, Oct 03 2013

%F From _Stefano Spezia_, Nov 30 2023: (Start)

%F O.g.f.: 6*(2 - 5*x)/((1 - x)*(1 - 10*x)).

%F E.g.f.: 2*exp(x)*(1 + 5*exp(9*x)).

%F (R(a(n)) + 1)/(a(n) - 1) = 2, where R(k) = A004086(k). (End)

%F a(n) = 6 * A126109(n). - _Alois P. Heinz_, Nov 30 2023

%t Table[FromDigits[Join[PadRight[{1},n,0],{2}]],{n,20}] (* or *) 10^Range[20]+2 (* or *) LinearRecurrence[{11,-10},{12,102},20] (* _Harvey P. Dale_, Oct 03 2013 *)

%o (Magma) [10^(n+1)+2: n in [0..20]]; // _Vincenzo Librandi_, Aug 10 2011

%Y Subsequence of A052148.

%Y Cf. A004086, A126109.

%K nonn,base,easy

%O 0,1

%A _Paul Curtz_, Oct 29 2007