A253213 a(n) = 10^n + 9.
10, 19, 109, 1009, 10009, 100009, 1000009, 10000009, 100000009, 1000000009, 10000000009, 100000000009, 1000000000009, 10000000000009, 100000000000009, 1000000000000009, 10000000000000009, 100000000000000009, 1000000000000000009, 10000000000000000009, 100000000000000000009
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Magma
[10^n+9: n in [0..30]];
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Mathematica
Table[10^n + 9, {n, 0, 40}] LinearRecurrence[{11,-10},{10,19},40] (* Harvey P. Dale, Jun 29 2018 *)
Formula
a(n) = 11*a(n-1) - 10*a(n-2) for n > 1.
G.f.: (10 - 91*x)/((1 - x)*(1 - 10*x)).
E.g.f.: exp(x)*(exp(9*x) + 9). - Elmo R. Oliveira, Sep 15 2024
Extensions
a(20) from Elmo R. Oliveira, Sep 15 2024
a(20) corrected by Sean A. Irvine, Sep 22 2024