%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