cp's OEIS Frontend

A074605 a(n) = 3^n + 4^n.

%I A074605 #30 Jan 16 2024 08:34:52
%S A074605 2,7,25,91,337,1267,4825,18571,72097,281827,1107625,4371451,17308657,
%T A074605 68703187,273218425,1088090731,4338014017,17309009347,69106897225,
%U A074605 276040168411,1102998412177,4408506864307,17623567104025
%N A074605 a(n) = 3^n + 4^n.
%C A074605 x^n + y^n = (x+y)*a(n-1) - (x*y)*a(n-2). - _Vincenzo Librandi_, Jul 19 2010
%D A074605 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 14.
%H A074605 B. Berselli, <a href="/A074605/b074605.txt">Table of n, a(n) for n = 0..1000</a>. - _Bruno Berselli_, Jul 20 2010
%H A074605 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12).
%F A074605 a(n) = A074506(n) - 1.
%F A074605 2 + 7*x + 25*x^2 + 91*x^3  + ... n terms = (1 - (4*x)^n)/(1 - 4*x) + (1 - (3*x)^n)/(1 - 3*x). [Jolley] - _Gary W. Adamson_, Dec 20 2006
%F A074605 From _Mohammad K. Azarian_, Jan 11 2009: (Start)
%F A074605 G.f.: 1/(1-3*x) + 1/(1-4*x).
%F A074605 E.g.f.: exp(3*x) + exp(4*x). (End)
%F A074605 a(n) = 3*a(n-1) + 4^(n-1). - _Bruno Berselli_, Jul 20 2010
%F A074605 a(n) = 7*a(n-1) - 12*a(n-2) with a(0)=2, a(1)=7. - _Vincenzo Librandi_, Jul 19 2010
%t A074605 Table[3^n + 4^n, {n, 0, 25}]
%o A074605 (PARI) a(n)=3^n+4^n \\ _Charles R Greathouse IV_, Oct 07 2015
%o A074605 (Magma) [3^n+4^n: n in [0..40]]; // _G. C. Greubel_, Jan 16 2024
%o A074605 (SageMath) [3^n+4^n for n in range(41)] # _G. C. Greubel_, Jan 16 2024
%Y A074605 Cf. A000051, A007689, A034472, A034474, A034491, A052539, A062394.
%Y A074605 Cf. A062395, A062396, A063376, A063481, A074506, A074600..A074624.
%K A074605 easy,nonn
%O A074605 0,1
%A A074605 _Robert G. Wilson v_, Aug 25 2002