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A307886 Array of coefficients of the minimal polynomial of (2*cos(Pi/15))^n, for n >= 1 (ascending powers).

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%I A307886 #16 May 18 2019 03:51:57
%S A307886 1,-4,-4,1,1,1,-24,26,-9,1,1,-109,-49,1,1,1,-524,246,-29,1,1,-2504,
%T A307886 -619,-4,1,1,-11979,2621,-99,1,1,-57299,-7774,-34,1,1,-274084,30126,
%U A307886 -349,1,1,-1311049,-97879,-179,1,1,-6271254,363131,-1254,1,1,-29997829,-1237504,-824,1
%N A307886 Array of coefficients of the minimal polynomial of (2*cos(Pi/15))^n, for n >= 1 (ascending powers).
%C A307886 The length of each row is 5.
%C A307886 The minimal polynomial of (2*cos(Pi/15))^n, for n >= 1, is C(15, n, x) = Product_{j=0..3} (x - (x_j)^n) = Sum_{k=0} T(n, k) x^k, where x_0 = 2*cos(Pi/15), x_1 = 2*cos(7*Pi/15), x_2 = 2*cos(11*Pi/15), and x_3 = 2*cos(13*Pi/15) are the zeros of C(15, 1, x) with coefficients given in A187360 (row n=15).
%F A307886 T(n,k) = the coefficient of x^k in C(15, n, x), n >= 1, k=0,1,2,3,4, with C(15, n, k) the minimal polynomial of (2*cos(Pi/15))^n, for n >= 1 as defined above.
%F A307886 T(n, 0) = T(n, 4) = 1. T(n, 1) = -A306610(n), T(n, 2) = A306611(n), T(n, 3) = -A306603(n), n >= 1.
%e A307886 The rectangular array T(n, k) begins:
%e A307886 n\k 0      1      2      3      4
%e A307886 ---------------------------------
%e A307886 1:  1     -4     -4      1      1
%e A307886 2:  1    -24     26     -9      1
%e A307886 3:  1   -109    -49      1      1
%e A307886 4:  1   -524    246    -29      1
%e A307886 5:  1  -2504   -619     -4      1
%e A307886 6:  1 -11979   2621    -99      1
%e A307886 7:  1 -57299  -7774    -34      1
%e A307886 ...
%t A307886 Flatten[Table[CoefficientList[MinimalPolynomial[(2*Cos[\[Pi]/15])^n, x], x], {n, 1, 15}]]
%Y A307886 Cf. A019887 (cos(Pi/15)), A019815 (cos(7*Pi/15)), A019851 (cos(11*Pi/15)), A019875 (cos(13*Pi/15)), A187360, A306603, A306610, A306611.
%K A307886 sign,tabf,easy
%O A307886 1,2
%A A307886 _Greg Dresden_ and _Wolfdieter Lang_, May 02 2019