A024128 a(n) = 11^n - n.
1, 10, 119, 1328, 14637, 161046, 1771555, 19487164, 214358873, 2357947682, 25937424591, 285311670600, 3138428376709, 34522712143918, 379749833583227, 4177248169415636, 45949729863572145, 505447028499293754, 5559917313492231463, 61159090448414546272, 672749994932560009181
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (13,-23,11).
Crossrefs
Programs
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Magma
[11^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
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Magma
I:=[1, 10, 119]; [n le 3 select I[n] else 13*Self(n-1)-23*Self(n-2)+11*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
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Mathematica
Table[11^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 12 x^2) / ((1 - 11 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *) LinearRecurrence[{13,-23,11},{1,10,119},20] (* Harvey P. Dale, Aug 02 2017 *) -
PARI
a(n)=11^n-n \\ Charles R Greathouse IV, Jul 01 2011
Formula
From Vincenzo Librandi, Jun 17 2013: (Start)
G.f.: (1-3*x+12*x^2)/((1-11*x) (1-x)^2).
a(n) = 13*a(n-1) - 23*a(n-2) + 11*a(n-3). (End)
E.g.f.: exp(x)*(exp(10*x) - x). - Elmo R. Oliveira, Sep 10 2024
Comments