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a(n) = (4^n + 20)/3.
3

%I #20 Jun 15 2023 11:33:53

%S 7,8,12,28,92,348,1372,5468,21852,87388,349532,1398108,5592412,

%T 22369628,89478492,357913948,1431655772,5726623068,22906492252,

%U 91625968988,366503875932,1466015503708,5864062014812,23456248059228,93824992236892,375299968947548

%N a(n) = (4^n + 20)/3.

%H Vincenzo Librandi, <a href="/A156605/b156605.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) = -A156591(2n+1).

%F a(n) = 4 + A154879(2n) = 7 + A002450(n).

%F a(n) = 4*a(n-1) - 20, n > 0.

%F G.f.: (7 - 27*x)/((1-x)*(1-4*x)). - _R. J. Mathar_, Feb 23 2009

%F E.g.f.: (1/3)*(20*exp(x) + exp(4*x)). - _G. C. Greubel_, Jun 25 2021

%t (4^Range[0,40] + 20)/3 (* _G. C. Greubel_, Jun 25 2021 *)

%o (Magma) [(4^n+20)/3: n in [0..35]]; // _Vincenzo Librandi_, Jul 24 2011

%o (Sage) [(4^n + 20)/3 for n in (0..40)] # _G. C. Greubel_, Jun 25 2021

%Y Cf. A002450, A154879, A156591.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Feb 11 2009

%E Edited and extended by _R. J. Mathar_, Feb 23 2009