A074611 - OEIS

%I #22 Jan 14 2024 02:30:40

%S 2,9,41,189,881,4149,19721,94509,456161,2215269,10814201,53022429,

%T 260917841,1287811989,6371951081,31591319949,156882857921,

%U 780119322309,3883416742361,19348364235069,96466943268401,481235204714229

%N a(n) = 4^n + 5^n.

%H Vincenzo Librandi, <a href="/A074611/b074611.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 (9,-20).

%F From _Mohammad K. Azarian_, Jan 11 2009: (Start)

%F G.f.: 1/(1-4*x) + 1/(1-5*x).

%F E.g.f.: exp(4*x) + exp(5*x). (End)

%F a(n) = 9*a(n-1) - 20*a(n-2), with n>1, a(0)=2, a(1)=9. - _Vincenzo Librandi_, Jul 21 2010

%t Table[4^n + 5^n, {n, 0, 25}]

%t CoefficientList[Series[1/(1 - 4 x) + 1/(1 - 5 x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 06 2013 *)

%o (Magma) [4^n + 5^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 06 2013

%o (SageMath) [4^+5^n for n in range(31)] # _G. C. Greubel_, Jan 13 2024

%Y Cf. A000051, A007689, A034472, A034474, A034491, A052539, A062394.

%Y Cf. A062395, A062396, A063376, A063481, A074600 - A074624.

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 25 2002