A074607 - OEIS

%I #26 Jan 15 2024 01:45:16

%S 2,9,45,243,1377,8019,47385,282123,1686177,10097379,60525225,

%T 362974203,2177313777,13062288339,78368947065,470199333483,

%U 2821152954177,16926788584899,101560344088905,609360902271963,3656161926847377

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

%H Vincenzo Librandi, <a href="/A074607/b074607.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-18).

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

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

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

%F a(n) = 9*a(n-1) - 18*a(n-2) with a(0)=2, a(1)=9. - _Vincenzo Librandi_, Jul 21 2010

%F G.f.: G(0), where G(k)= 1 + 2^k/(1 - 3*x/(3*x + 2^k/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jul 22 2013

%t Table[3^n + 6^n, {n, 0, 25}]

%o (Magma) [3^n + 6^n: n in [0..35]]; // _Vincenzo Librandi_, Apr 30 2011

%o (SageMath) [3^n+6^n for n in range(41)] # _G. C. Greubel_, Jan 14 2024

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

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 25 2002