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a(n) = 5^n + 9^n.
0

%I #16 Aug 02 2024 15:07:55

%S 2,14,106,854,7186,62174,547066,4861094,43437346,389373614,3496550026,

%T 31429887734,282673677106,2543086531454,22882895970586,

%U 205921649672774,1853172776742466,16677944639119694,150098449994264746

%N a(n) = 5^n + 9^n.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (14,-45).

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

%F G.f.: 1/(1-5*x) + 1/(1-9*x).

%F E.g.f.: e^(5*x) + e^(9*x). (End)

%F a(n) = 14*a(n-1) - 45*a(n-2) with a(0)=2, a(1)=14. - _Vincenzo Librandi_, Jul 21 2010

%t Table[5^n + 9^n, {n, 0, 20}]

%t LinearRecurrence[{14,-45},{2,14},20] (* _Harvey P. Dale_, Aug 02 2024 *)

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

%K easy,nonn

%O 0,1

%A _Robert G. Wilson v_, Aug 26 2002