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A275546 a(n) = (tan(1*Pi/11))^(2*n)+(tan(2*Pi/11))^(2*n)+(tan(3*Pi/11))^(2*n)+(tan(4*Pi/11))^(2*n)+(tan(5*Pi/11))^(2*n). 1

%I

%S 5,55,2365,113311,5476405,264893255,12813875437,619859803695,

%T 29985188632421,1450508002869079,70167091762786205,

%U 3394273427239643839,164195092176119969173,7942798031108524622951,384226104001681151724877,18586611219134532494467151,899111520569015285343455941,43493755633501102693569684087,2103973462501643822799172235773

%N a(n) = (tan(1*Pi/11))^(2*n)+(tan(2*Pi/11))^(2*n)+(tan(3*Pi/11))^(2*n)+(tan(4*Pi/11))^(2*n)+(tan(5*Pi/11))^(2*n).

%C (tan(1*Pi/11))^(2*n),(tan(2*Pi/11))^(2*n),(tan(3*Pi/11))^(2*n),

%C (tan(4*Pi/11))^(2*n),(tan(5*Pi/11))^(2*n) are roots of the polynomial x^5 - 55x^4 + 330x^3 - 462x^2 + 165x - 11.

%H Colin Barker, <a href="/A275546/b275546.txt">Table of n, a(n) for n = 0..550</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (55,-330,462,-165,11).

%F a(-2) = 141, a(-1) = 15, a(0) = 5, a(1) = 55, a(2) = 2365.

%F a(n) = +55*a(n-1)-330*a(n-2)+462*a(n-3)-165*a(n-4)-11*a(n-5) for n > 2.

%F a(n) ~ k^n where k = 48.37415... is the largest real root of x^5 - 55x^4 + 330x^3 - 462x^2 + 165x - 11. - _Charles R Greathouse IV_, Aug 01 2016

%F G.f.: (5-220*x+990*x^2-924*x^3+165*x^4) / (1-55*x+330*x^2-462*x^3+165*x^4-11*x^5). - _Colin Barker_, Aug 02 2016

%o (PARI) a(n)=([0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1;11,-165,462,-330,55]^n*[5;55;2365;113311;5476405])[1,1] \\ _Charles R Greathouse IV_, Aug 01 2016

%o (PARI) Vec((5-220*x+990*x^2-924*x^3+165*x^4)/(1-55*x+330*x^2-462*x^3+165*x^4-11*x^5) + O(x^20)) \\ _Colin Barker_, Aug 02 2016

%K nonn,easy

%O 0,1

%A _Kai Wang_, Aug 01 2016

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Last modified August 4 13:49 EDT 2020. Contains 336201 sequences. (Running on oeis4.)