%I #24 Sep 08 2022 08:45:07

%S 2,13,85,559,3697,24583,164305,1103479,7444417,50431303,342941425,

%T 2340123799,16018069537,109949704423,756587236945,5217746494519,

%U 36054040477057,249557173431943,1729973554578865,12008254925383639

%N a(n) = 6^n + 7^n.

%H Vincenzo Librandi, <a href="/A074619/b074619.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-42).

%F G.f.: 1/(1-6*x)+1/(1-7*x). E.g.f.: e^(6*x)+e^(7*x). - _Mohammad K. Azarian_, Jan 11 2009

%F a(n)=13*a(n-1)-42*a(n-2) with a(0)=2, a(1)=13. - _Vincenzo Librandi_, Jul 21 2010

%t Table[6^n + 7^n, {n, 0, 20}]

%t CoefficientList[Series[1/(1 - 6*x) + 1/(1 - 7*x), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jan 11 2013 *)

%t LinearRecurrence[{13,-42},{2,13},30] (* _Harvey P. Dale_, Mar 30 2019 *)

%o (Magma) [7^n+6^n: n in [0..20]]; // _Vincenzo Librandi_, Jan 11 2013

%o (PARI) a(n)=6^n+7^n \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600-A074624.

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 26 2002