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a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.
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%I #7 Sep 08 2022 08:45:46

%S 5,23,119,653,3677,20927,119615,684869,3923957,22488359,128895431,

%T 738814781,4234877645,24274429007,139142022671,797568604277,

%U 4571702539493,26205228460343,150209694669335,861009587370221

%N a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.

%C Binomial transform of A162814. Inverse binomial transform of A143647.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13)

%F a(n) = ((5+sqrt(3))*(4+sqrt(3))^n+(5-sqrt(3))*(4-sqrt(3))^n)/2.

%F G.f.: (5-17*x)/(1-8*x+13*x^2).

%t LinearRecurrence[{8,-13},{5,23},20] (* _Harvey P. Dale_, Aug 25 2017 *)

%o (Magma) [ n le 2 select 18*n-13 else 8*Self(n-1)-13*Self(n-2): n in [1..20] ];

%Y Cf. A162814, A143647.

%K nonn,easy

%O 0,1

%A _Klaus Brockhaus_, Jul 18 2009