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a(n) = 2^n + 8^n + 9^n.
1

%I #18 Sep 08 2022 08:45:07

%S 3,19,149,1249,10673,91849,793649,6880249,59824193,521638729,

%T 4560527249,39970996249,351149017313,3091621650409,27274838982449,

%U 241075504216249,2134495165628033,18928981513482889,168109033806743249

%N a(n) = 2^n + 8^n + 9^n.

%H Vincenzo Librandi, <a href="/A074546/b074546.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (19,-106,144).

%F From _Mohammad K. Azarian_, Dec 28 2008: (Start)

%F G.f.: 1/(1-2*x) + 1/(1-8*x) + 1/(1-9*x).

%F E.g.f.: exp(2*x) + exp(8*x) + exp(9*x). (End)

%F a(n) = 19*a(n-1) - 106*a(n-2) + 144*a(n-3).

%t Table[2^n + 8^n + 9^n, {n, 0, 20}]

%t LinearRecurrence[{19,-106,144},{3,19,149},20] (* _Harvey P. Dale_, May 31 2013 *)

%o (Magma) [ 2^n + 8^n + 9^n: n in [0..30]]; // _Vincenzo Librandi_, Jun 13 2011

%Y Cf. A001550, A001576, A034513, A001579, A074501 - A074580.

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 23 2002