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A155130 a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48. 11

%I #13 Dec 31 2023 10:22:40

%S 1,6,48,378,2982,23520,185514,1463238,11541264,91031514,718009446,

%T 5663286720,44669073162,352326519174,2778969146352,21919069658682,

%U 172886271635238,1363637389057440,10755665624848746,84835121097343302

%N a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48.

%H G. C. Greubel, <a href="/A155130/b155130.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 (7,7).

%F G.f.: (1-x-x^2)/(1-7*x-7*x^2) .

%F a(n) = (1/7)*[n=0] - 6*(sqrt(7)*i)^(n-2)*ChebyshevU(n, -sqrt(7)*i/2). - _G. C. Greubel_, Mar 25 2021

%p m:= 7; 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[{7,7},{1,6,48},30] (* _Harvey P. Dale_, Mar 11 2018 *)

%o (Magma) m:=7; [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=7; [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), A155127 (m=6), this sequence (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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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)