A199691 a(n) = 11*10^n + 1.
12, 111, 1101, 11001, 110001, 1100001, 11000001, 110000001, 1100000001, 11000000001, 110000000001, 1100000000001, 11000000000001, 110000000000001, 1100000000000001, 11000000000000001, 110000000000000001, 1100000000000000001, 11000000000000000001, 110000000000000000001
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Crossrefs
Cf. A199690.
Programs
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Magma
[11*10^n+1: n in [0..30]];
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Mathematica
11 10^Range[0,20]+1 (* or *) LinearRecurrence[{11,-10},{12,111},20] (* Harvey P. Dale, Jan 29 2023 *)
Formula
a(n) = 10*a(n-1) - 9.
a(n) = 11*a(n-1) - 10*a(n-2).
G.f.: 3*(4-7*x)/((1-x)*(1-10*x)).
From Elmo R. Oliveira, Jun 10 2025: (Start)
E.g.f.: exp(x)*(1 + 11*exp(9*x)).
a(n) = 3*A199690(n). (End)