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A216450 a(n) = -10*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 3, a(1) = -20, and a(2) = 94. 4

%I

%S 3,-10,94,-907,8778,-84965,822409,-7960417,77051978,-745816120,

%T 7219044849,-69875948152,676356530853,-6546718419225,63368238651539,

%U -613365874726862,5937007312894778,-57466607266115655,556241684847745354,-5384080019366211797

%N a(n) = -10*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 3, a(1) = -20, and a(2) = 94.

%C a(n) = (a/b)^n + (b/c)^n + (c/a)^n, where a = cos(Pi/13) + cos(5*Pi/13), b = cos(3*Pi/13) + cos(11*Pi/13), and c = cos(7*Pi/13) + cos(9*Pi/13).

%C The Berndt-type sequence number 11 for the argument 2Pi/13. I am very grateful Sergey Markelov and http://ru-math.livejournal.com/797774.html for his and its respectively inspiration for creating this sequence.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (-10,-3,1).

%F a(n) = -10*a(n-1)-3*a(n-2)+a(n-3). G.f.: -(3*x^2+20*x+3) / (x^3-3*x^2-10*x-1). - _Colin Barker_, Jun 01 2013

%t LinearRecurrence[{-10, -3, 1}, {3, -10, 94}, 20] (* _T. D. Noe_, Sep 17 2012 *)

%K sign,easy

%O 0,1

%A _Roman Witula_, Sep 15 2012

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Last modified August 10 12:19 EDT 2020. Contains 336379 sequences. (Running on oeis4.)