A191466 a(n) = 9^n - 5^n.
0, 4, 56, 604, 5936, 55924, 515816, 4704844, 42656096, 385467364, 3477018776, 31332231484, 282185395856, 2540645125204, 22870688939336, 205860614516524, 1852867600961216, 16676418760213444, 150090820599733496, 1350832644186663964, 12157570091625288176, 109418512294354156084
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (14,-45).
Programs
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Magma
[9^n-5^n: n in [0..20]];
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Mathematica
Table[9^n - 5^n, {n, 0, 25}] (* or *) CoefficientList[Series[4 x/((1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *) LinearRecurrence[{14,-45},{0,4},20] (* Harvey P. Dale, Jun 26 2019 *) -
PARI
a(n)=9^n-5^n \\ Charles R Greathouse IV, Jun 08 2011
Formula
a(n) = 14*a(n-1) - 45*a(n-2).
From Vincenzo Librandi, Oct 05 2014: (Start)
G.f.: 4*x/((1-5*x)*(1-9*x)).
a(n+1) = 4*A016163(n). (End)
E.g.f.: 2*exp(14*x/2)*sinh(2*x). - Elmo R. Oliveira, Mar 31 2025