%I #27 Mar 11 2023 08:14:31
%S 2,13,97,793,6817,60073,535537,4799353,43112257,387682633,3487832977,
%T 31385253913,282446313697,2541932937193,22877060890417,
%U 205892205836473,1853024483819137,16677198879535753,150094704016475857
%N a(n) = 4^n + 9^n.
%H G. C. Greubel, <a href="/A074614/b074614.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-36).
%F a(n) = 2^(2*n) + 3^(2*n).
%F G.f.: (2-13*x)/((1-4*x)*(1-9*x)).
%F E.g.f.: e^(4*x) + e^(10*x). - _Mohammad K. Azarian_, Jan 11 2009
%F a(n) = 13*a(n-1) - 36*a(n-2) with a(0)=2, a(1)=13. - _Vincenzo Librandi_, Jul 21 2010
%t Table[4^n + 9^n, {n, 0, 25}]
%t LinearRecurrence[{13,-36},{2,13},30] (* _Harvey P. Dale_, Aug 11 2017 *)
%o (PARI) a(n)=4^n+9^n \\ _Charles R Greathouse IV_, Jul 01 2016
%o (Magma) [4^n+9^n: n in [0..30]]; // _G. C. Greubel_, Mar 10 2023
%o (SageMath) [4^n+9^n for n in range(31)] # _G. C. Greubel_, Mar 10 2023
%Y Cf. A000051, A034472, A034474, A034491, A052539, A062394, A062395.
%Y Cf. A062396, A063376, A063481, A074600..A074624.
%Y Bisection of A007689 (even-indexed members).
%K easy,nonn
%O 0,1
%A _Robert G. Wilson v_, Aug 26 2002