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A106567 a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.

%I A106567 #28 Jan 19 2025 11:32:11
%S A106567 0,4,20,116,660,3764,21460,122356,697620,3977524,22678100,129300596,
%T A106567 737215380,4203279284,23965257940,136639406836,779058065940,
%U A106567 4441847957044,25325472048980,144394752073076,823275648561300,4693957251098804,26762888849739220
%N A106567 a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.
%H A106567 Vincenzo Librandi, <a href="/A106567/b106567.txt">Table of n, a(n) for n = 0..1000</a>
%H A106567 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,4).
%F A106567 a(n) = 4*A015537(n).
%F A106567 From _Chai Wah Wu_, Mar 21 2018: (Start)
%F A106567 a(n) = 5*a(n-1) + 4*a(n-2) for n > 1.
%F A106567 G.f.: 4*x/(1 - 5*x - 4*x^2). (End)
%F A106567 a(n) = 4*(p^n - q^n)/(p - q), where 2*p = 5 + sqrt(41), 2*q = 5 - sqrt(41). - _G. C. Greubel_, Sep 06 2021
%t A106567 CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Mar 22 2018 *)
%t A106567 LinearRecurrence[{5,4},{0,4},30] (* _Harvey P. Dale_, Jan 19 2025 *)
%o A106567 (Magma)  I:=[0,4]; [n le 2 select I[n] else 5*Self(n-1) +4*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Mar 22 2018
%o A106567 (PARI) a(n) = (([0,4; 1,5]^n)*[0,1]~)[1]; \\ _Michel Marcus_, Mar 22 2018
%o A106567 (Sage)
%o A106567 def A106567_list(prec):
%o A106567     P.<x> = PowerSeriesRing(ZZ, prec)
%o A106567     return P( 4*x/(1-5*x-4*x^2) ).list()
%o A106567 A106567_list(30) # _G. C. Greubel_, Sep 06 2021
%Y A106567 Cf. A015537.
%K A106567 nonn,easy,less
%O A106567 0,2
%A A106567 _Roger L. Bagula_, May 30 2005
%E A106567 Edited by _N. J. A. Sloane_, Apr 30 2006
%E A106567 New name after Chai Wah Wu, by _Bruno Berselli_, Mar 22 2018