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