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%I #9 Jun 14 2023 18:28:57
%S 2,3,7,23,87,343,1367,5463,21847,87383,349527,1398103,5592407,
%T 22369623,89478487,357913943,1431655767,5726623063,22906492247,
%U 91625968983,366503875927,1466015503703,5864062014807,23456248059223,93824992236887,375299968947543
%N a(n) = (4^n + 5)/3.
%H G. C. Greubel, <a href="/A163834/b163834.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^n + 5)/3 = A135351(2*n+1) = A140966(2*n) = A153643(2*n).
%F a(n) = 5*a(n-1) - 4*a(n-2).
%F G.f.: (2-7*x)/((4*x-1)*(x-1)).
%F a(n+1) - a(n) = A000302(n).
%F E.g.f.: (1/3)*(5*exp(x) + exp(4*x)). - _G. C. Greubel_, Aug 05 2017
%t Table[(4^n + 5)/3, {n, 0, 50}] (* _G. C. Greubel_, Aug 05 2017 *)
%t LinearRecurrence[{5,-4},{2,3},30] (* _Harvey P. Dale_, Jun 14 2023 *)
%o (PARI) x='x+O('x^50); concat([0], Vec((2-7*x)/((4*x-1)*(x-1)))) \\ _G. C. Greubel_, Aug 05 2017
%Y Cf. A000027, A135351, A140966, A153643.
%K nonn,easy
%O 0,1
%A _Juri-Stepan Gerasimov_, Aug 05 2009
%E Offset set to 0 by _R. J. Mathar_, Aug 06 2009
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