%I #8 Sep 10 2023 12:18:10
%S 4,5,9,25,89,345,1369,5465,21849,87385,349529,1398105,5592409,
%T 22369625,89478489,357913945,1431655769,5726623065,22906492249,
%U 91625968985,366503875929,1466015503705,5864062014809,23456248059225,93824992236889,375299968947545
%N a(n) = (4^n + 11)/3.
%H G. C. Greubel, <a href="/A163868/b163868.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F a(n) = 4*a(n-1) - 11 = A155701(n) + 1 = A163834(n) + 2 = A047849(n) + 3.
%F From _R. J. Mathar_, Aug 11 2009: (Start)
%F a(n)= 5*a(n-1) - 4*a(n-2).
%F G.f.: (4 - 15*x)/((4*x-1)*(x-1)). (End)
%F E.g.f.: (1/3)*(exp(4*x) + 11*exp(x)). - _G. C. Greubel_, Aug 06 2017
%t LinearRecurrence[{5,-4}, {4,5}, 50] (* _G. C. Greubel_, Aug 06 2017 *)
%t (4^Range[0,30]+11)/3 (* _Harvey P. Dale_, Sep 10 2023 *)
%o (PARI) x='x+O('x^50); Vec((4 - 15*x)/((4*x-1)*(x-1))) \\ _G. C. Greubel_, Aug 06 2017
%Y Cf. A002450, A047849, A156605.
%K nonn,easy
%O 0,1
%A _Juri-Stepan Gerasimov_, Aug 08 2009
%E a(11) corrected by _R. J. Mathar_, Aug 11 2009