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A051958 a(n) = 2*a(n-1) + 24*a(n-2), a(0)=0, a(1)=1.

%I A051958 #37 Nov 11 2024 05:18:18
%S A051958 0,1,2,28,104,880,4256,29632,161408,1033984,5941760,36699136,
%T A051958 216000512,1312780288,7809572864,47125872640,281681494016,
%U A051958 1694383931392,10149123719168,60963461791744,365505892843520,2194134868688896
%N A051958 a(n) = 2*a(n-1) + 24*a(n-2), a(0)=0, a(1)=1.
%H A051958 Vincenzo Librandi, <a href="/A051958/b051958.txt">Table of n, a(n) for n = 0..200</a>
%H A051958 Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689_Extending_the_Golden_Ratio_and_the_Binet-de_Moivre_Formula">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H A051958 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,24).
%F A051958 G.f.: x/((1+4*x)*(1-6*x)).
%F A051958 a(n) = (6^n - (-4)^n)/10.
%F A051958 a(n) = 2^(n-1)*A015441(n).
%F A051958 a(n+1) = Sum_{k = 0..n} A238801(n,k)*5^k. - _Philippe Deléham_, Mar 07 2014
%F A051958 Limit_{n -> oo} a(n+1)/a(n) = 6. - _Felix P. Muga II_, Mar 10 2014
%F A051958 E.g.f.: (1/10)*(exp(6*x) - exp(-4*x)). - _G. C. Greubel_, Nov 11 2024
%t A051958 Table[(6^n-(-4)^n)/10, {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 01 2011 *)
%t A051958 CoefficientList[Series[x/((1+4 x) (1-6 x)), {x,0,30}], x] (* _Vincenzo Librandi_, Mar 08 2014 *)
%t A051958 LinearRecurrence[{2,24},{0,1},30] (* _Harvey P. Dale_, May 08 2022 *)
%o A051958 (PARI) a(n)=(6^n-(-4)^n)/10
%o A051958 (Magma) [(6^n-(-4)^n)/10: n in [0..30]]; // _Vincenzo Librandi_, Mar 08 2014
%o A051958 (SageMath)
%o A051958 A051958=BinaryRecurrenceSequence(2,24,0,1)
%o A051958 [A051958(n) for n in range(31)] # _G. C. Greubel_, Nov 11 2024
%Y A051958 Cf. A015441, A238801.
%K A051958 easy,nonn
%O A051958 0,3
%A A051958 _Barry E. Williams_, Jan 04 2000