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a(n) = 3^n + 4^n + 6^n.
1

%I #20 May 26 2024 02:19:47

%S 3,13,61,307,1633,9043,51481,298507,1751713,10359523,61573801,

%T 367168507,2194090993,13129397203,78637382521,471273075307,

%U 2825447921473,16943968454083,101629063565641,609635780178907

%N a(n) = 3^n + 4^n + 6^n.

%H Vincenzo Librandi, <a href="/A074548/b074548.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-54,72).

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

%F G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-6*x).

%F E.g.f.: exp(3*x) + exp(4*x) + exp(6*x). (End)

%F a(n) = 13*a(n-1) - 54*a(n-2) + 72*a(n-3).

%t Table[3^n + 4^n + 6^n, {n, 0, 21}]

%t LinearRecurrence[{13,-54,72},{3,13,61},30] (* _Harvey P. Dale_, Dec 21 2022 *)

%o (Magma) [3^n + 4^n + 6^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