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%I #20 Dec 31 2023 10:22:30
%S 1,4,24,140,820,4800,28100,164500,963000,5637500,33002500,193200000,
%T 1131012500,6621062500,38760375000,226907187500,1328337812500,
%U 7776225000000,45522814062500,266495195312500,1560090046875000,9132926210937500
%N a(n) = 5*a(n-1) + 5*a(n-2), n > 2, a(0)=1, a(1)=4, a(2)=24.
%H G. C. Greubel, <a href="/A155119/b155119.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 (5,5).
%F G.f.: (1 - x - x^2) / (1 - 5*x - 5*x^2).
%F a(n) = (1/5)*[n=0] - 4*(sqrt(5)*i)^(n-2)*ChebyshevU(n, -sqrt(5)*i/2). - _G. C. Greubel_, Mar 25 2021
%F E.g.f.: (3 + 4*exp(5*x/2)*(3*cosh(3*sqrt(5)*x/2) + sqrt(5)*sinh(3*sqrt(5)*x/2)))/15. - _Stefano Spezia_, May 31 2023
%t With[{m=5}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* _G. C. Greubel_, Mar 25 2021 *)
%o (Magma) m:=5; [1] cat [n le 2 select (m-1)*(m*n-(m-1)) else m*(Self(n-1) + Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Mar 25 2021
%o (Sage) m=5; [1]+[-(m-1)*(sqrt(m)*i)^(n-2)*chebyshev_U(n, -sqrt(m)*i/2) for n in (1..30)] # _G. C. Greubel_, Mar 25 2021
%Y Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), this sequence (m=5), A155127 (m=6), A155130 (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Jan 20 2009
%E a(20) corrected and a(21) from _Sean A. Irvine_, May 19 2019
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