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%I #4 Jan 09 2016 19:59:27
%S -14,-90,-722,-4830,-33554,-228954,-1572110,-10768122,-73825010,
%T -505954014,-3467991794,-23769625530,-162920337422,-1116670248090,
%U -7653777913874,-52459758093534,-359564573392850,-2464492138756122,-16891880703949070,-115778671987640634
%N Coefficient of x in the minimal polynomial of the continued fraction [1^n,sqrt(6),1,1,...], where 1^n means n ones.
%C See A265762 for a guide to related sequences.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,15,-15,-5,1).
%F a(n) = 5*a(n-1) + 15*a(n-2) - 15*a(n-3) - 5*a(n-4) + a(n-5) .
%F G.f.: -((2 (-7 - 10 x - 31 x^2 - 40 x^3 + 3 x^4))/(-1 + 5 x + 15 x^2 - 15 x^3 - 5 x^4 + x^5)).
%e Let p(n,x) be the minimal polynomial of the number given by the n-th continued fraction:
%e [sqrt(6),1,1,1,...] has p(0,x) = 19-14x-13x^2+2x^3+x^4, so a(0) = -14;
%e [1,sqrt(6),1,1,1,...] has p(1,x) = 19-90x+143x^2-90x^3+19x^4, so a(1) = -90;
%e [1,1,sqrt(6),1,1,1...] has p(2,x) = 361-722x+527x^2-166x^3+19x^4, so a(2) = -722.
%t u[n_] := Table[1, {k, 1, n}]; t[n_] := Join[u[n], {Sqrt[6]}, {{1}}];
%t f[n_] := FromContinuedFraction[t[n]];
%t t = Table[MinimalPolynomial[f[n], x], {n, 0, 40}];
%t Coefficient[t, x, 0] ; (* A266804 *)
%t Coefficient[t, x, 1]; (* A266805 *)
%t Coefficient[t, x, 2]; (* A266806 *)
%t Coefficient[t, x, 3]; (* A266807 *)
%t Coefficient[t, x, 4]; (* A266804 *)
%Y Cf. A265762, A266804, A266806, A266807.
%K easy,sign
%O 0,1
%A _Clark Kimberling_, Jan 09 2016
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