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a(n) = 1^n + 5^n + 6^n.
1

%I #21 Sep 08 2022 08:45:07

%S 3,12,62,342,1922,10902,62282,358062,2070242,12030822,70231802,

%T 411625182,2420922962,14281397142,84467679722,500702562702,

%U 2973697798082,17689598897862,105374653934042,628433226338622

%N a(n) = 1^n + 5^n + 6^n.

%H Vincenzo Librandi, <a href="/A074516/b074516.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-41,30).

%F G.f.: 1/(1-x)+1/(1-5*x)+1/(1-6*x). E.g.f.: e^x+e^(5*x)+e^(6*x). [_Mohammad K. Azarian_, Dec 26 2008]

%F a(n) = 11*a(n-1) - 30*a(n-2) + 20, n>1. [_Gary Detlefs_, Jun 21 2010]

%p A074516:=n->1^n+5^n+6^n: seq(A074516(n), n=0..30); # _Wesley Ivan Hurt_, Jan 27 2017

%t Table[1^n + 5^n + 6^n, {n, 0, 20}]

%t LinearRecurrence[{12,-41,30},{3,12,62},20] (* _Harvey P. Dale_, Apr 06 2018 *)

%o (Magma) [5^n+6^n+1^n: n in [0..30]]; // _Vincenzo Librandi_, Mar 24 2013

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

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 23 2002