A191468 a(n) = 8^n - 5^n.
0, 3, 39, 387, 3471, 29643, 246519, 2019027, 16386591, 132264603, 1063976199, 8541106467, 68475336111, 548535110763, 4391942995479, 35153854510707, 281322388820031, 2251036874232123, 18010583812216359, 144096114589527747, 1152826137175206351, 9222895199696572683
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (13,-40).
Programs
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Magma
[8^n - 5^n: n in [0..20]];
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Mathematica
Table[8^n-5^n,{n,0,20}] (* or *) LinearRecurrence[{13,-40},{0,3},30] (* Harvey P. Dale, Dec 04 2012 *) CoefficientList[Series[3 x/((1 - 5 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *) -
PARI
a(n)=8^n-5^n \\ Charles R Greathouse IV, Jun 08 2011
Formula
a(n) = 13*a(n-1) - 40*a(n-2).
From Vincenzo Librandi, Oct 05 2014: (Start)
G.f.: 3*x/((1-5*x)*(1-8*x)).
a(n+1) = 3*A016162(n). (End)
E.g.f.: 2*exp(13*x/2)*sinh(3*x/2). - Elmo R. Oliveira, Mar 31 2025