A133384 Numbers with n 0's between 1 and 2.
12, 102, 1002, 10002, 100002, 1000002, 10000002, 100000002, 1000000002, 10000000002, 100000000002, 1000000000002, 10000000000002, 100000000000002, 1000000000000002, 10000000000000002, 100000000000000002, 1000000000000000002, 10000000000000000002
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Magma
[10^(n+1)+2: n in [0..20]]; // Vincenzo Librandi, Aug 10 2011
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Mathematica
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 *)
Formula
a(n) = 10^(n+1) + 2. - Vincenzo Librandi, Aug 10 2011
a(n) = 11*a(n-1) - 10*a(n-2); a(0)=12, a(1)=102. - Harvey P. Dale, Oct 03 2013
From Stefano Spezia, Nov 30 2023: (Start)
O.g.f.: 6*(2 - 5*x)/((1 - x)*(1 - 10*x)).
E.g.f.: 2*exp(x)*(1 + 5*exp(9*x)).
(R(a(n)) + 1)/(a(n) - 1) = 2, where R(k) = A004086(k). (End)
a(n) = 6 * A126109(n). - Alois P. Heinz, Nov 30 2023
Comments