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%I #14 Dec 31 2023 10:22:34
%S 1,5,35,240,1650,11340,77940,535680,3681720,25304400,173916720,
%T 1195326720,8215460640,56464724160,388081108800,2667274997760,
%U 18332136639360,125996469822720,865971638772480,5951808651571200
%N a(n) = 6*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=5, a(2)=35.
%H G. C. Greubel, <a href="/A155127/b155127.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 (6,6).
%F G.f.: (1-x-x^2)/(1-6*x-6*x^2) .
%F a(n) = (1/6)*[n=0] - 5*(sqrt(6)*i)^(n-2)*ChebyshevU(n, -sqrt(6)*i/2). - _G. C. Greubel_, Mar 25 2021
%p m:=6; 1,seq(simplify((1-m)*(sqrt(m)*I)^(n-2)*ChebyshevU(n, -I*sqrt(m)/2)), n = 1..30); # _G. C. Greubel_, Mar 25 2021
%t LinearRecurrence[{6,6},{1,5,35},20] (* _Harvey P. Dale_, Apr 14 2015 *)
%o (Magma) m:=6; [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=6; [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), A155119 (m=5), this sequence (m=6), A155130 (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).
%K nonn
%O 0,2
%A _Philippe Deléham_, Jan 20 2009
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