A074560 a(n) = 3^n + 8^n + 9^n.
3, 20, 154, 1268, 10738, 92060, 794314, 6882308, 59830498, 521657900, 4560585274, 39971171348, 351149544658, 3091623236540, 27274843749034, 241075518532388, 2134495208609218, 18928981642491980, 168109034193901594, 1494966906911109428, 13310586967150560178
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (20,-123,216).
Programs
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Magma
[3^n + 8^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011
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Maple
A074560:=n->3^n + 8^n + 9^n: seq(A074560(n), n=0..25); # Wesley Ivan Hurt, Aug 15 2016
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Mathematica
Table[3^n + 8^n + 9^n, {n, 0, 20}] LinearRecurrence[{20,-123,216}, {3, 20, 154}, 25] (* G. C. Greubel, Aug 15 2016 *)
Formula
From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-8*x) + 1/(1-9*x).
E.g.f.: exp(3*x) + exp(8*x) + exp(9*x). (End)
a(n) = 20*a(n-1) - 123*a(n-2) + 216*a(n-3) for n>2. - Wesley Ivan Hurt, Aug 15 2016