A221911 a(n) = 9^n + 9*n.
1, 18, 99, 756, 6597, 59094, 531495, 4783032, 43046793, 387420570, 3486784491, 31381059708, 282429536589, 2541865828446, 22876792455087, 205891132094784, 1853020188851985, 16677181699666722, 150094635296999283, 1350851717672992260, 12157665459056928981
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-19,9).
Programs
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Magma
[9^n + 9*n: n in [0..25]];
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Magma
I:=[1, 18, 99]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]];
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Mathematica
Table[(9^n + 9 n), {n, 0, 25}] (* or *) CoefficientList[Series[(1 + 7 x - 80 x^2)/((1 - x)^2 (1 - 9 x)), {x, 0, 30}], x] LinearRecurrence[{11,-19,9},{1,18,99},20] (* Harvey P. Dale, Aug 18 2014 *) -
PARI
a(n)=9^n+9*n \\ Charles R Greathouse IV, Apr 18 2013
Formula
G.f.: (1+7*x-80*x^2)/((1-x)^2*(1-9*x)).
a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
E.g.f.: exp(x)*(exp(8*x) + 9*x). - Elmo R. Oliveira, Sep 09 2024