A016188 - OEIS

%I #29 Nov 14 2024 08:20:51

%S 1,20,304,4160,54016,680960,8433664,103301120,1256390656,15210905600,

%T 183604609024,2211845242880,26610862391296,319880104509440,

%U 3842959300624384,46150695979581440,554089826731687936,6651329720593940480,79833971045636767744,958151767735717068800

%N Expansion of 1/((1-8*x)*(1-12*x)).

%H Paolo Xausa, <a href="/A016188/b016188.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-96).

%F a(n) = 3*12^n - 2*8^n. - _Bruno Berselli_, Feb 09 2011

%F a(n) = 12*a(n-1) + 8^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011

%F a(n) = 20*a(n-1) - 96*a(n-2), a(0)=1, a(1)=20. - _Vincenzo Librandi_, Feb 09 2011

%F E.g.f.: 3*exp(12*x) - 2*exp(8*x). - _G. C. Greubel_, Nov 14 2024

%t A016188[n_] := 3*12^n - 2*8^n; Array[A016188, 20, 0] (*  or *)

%t LinearRecurrence[{20, -96}, {1, 20}, 20] (* _Paolo Xausa_, Feb 08 2024 *)

%o (Magma) [4^n*(3^(n+1)-2^(n+1)): n in [0..40]]; // _G. C. Greubel_, Nov 14 2024

%o (SageMath)

%o A016188=BinaryRecurrenceSequence(20,-96,1,20)

%o print([A016188(n) for n in range(41)]) # _G. C. Greubel_, Nov 14 2024

%Y Cf. A016140.

%K nonn,changed

%O 0,2

%A _N. J. A. Sloane_