cp's OEIS Frontend

A231183 Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the first power.

%I A231183 #9 Jun 13 2015 00:54:54
%S A231183 0,-1,0,0,0,3,2,14,13,54,61,198,255,715,1012,2574,3910,9280,14877,
%T A231183 33557,56069,121736,209990,442933,783035,1615658,2910765,5905483,
%U A231183 10795397,21621095,39969597,79262102,147796497,290868226,545980212,1068246916
%N A231183 Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the first power.
%C A231183 The formula for rho(11)^n is (see A231182): rho(11)^n = A231182(n)*1 - a(n)*rho(11) - A231184(n-2)*rho(11)^2 + A231185(n-3)*rho(11)^3 + A231182(n+1)*rho(11)^4, n >= 0.
%H A231183 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-3,1).
%F A231183 G.f.: x*(-1 + x + 4*x^2 -3*x^3)/(1-x-4*x^2+3*x^3+3*x^4-x^5).
%F A231183 a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 5, with a(0)=0, a(1)=-1, a(2)=a(3)=a(4)=0.
%F A231183 a(n) = -b(n-1) + b(n-2) + 4*b(n-3) - 3*b(n-4) for n>=0, with b(n) = A231181(n).
%e A231183 rho(11)^5 = 1*1 - 3*rho(11) - 3*rho(11)^2 + 4*rho(11)^3 + 1*rho(11)^4. Approximately 26.02309649, with rho(11) approximately 1.918985947.
%Y A231183 Cf. A231181, A231182, A231184, A231185.
%K A231183 sign,easy
%O A231183 0,6
%A A231183 _Wolfdieter Lang_, Nov 07 2013