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A063780 a(n) is the number of pairs of integer quadruples (b_1, b_2, b_3, b_4) and (c_1, c_2, c_3, c_4) satisfying 1 <= b_1 < b_2 < b_3 < b_4 < n, 1 <= c_1 < c_2 < c_3 < c_4 < n, b_i != c_j for all i,j = 1,2,3,4 and Product_{i=1..4} cos(2*Pi*b_i/n) = Product_{i=1..4} cos(2*Pi*c_i/n).

%I A063780 #14 May 30 2023 23:13:31
%S A063780 0,1,3,4,9,9,18,17,93,29,84,45,433,66,253,93,1274,126,534,166,2940,
%T A063780 214,1120,270,5866,335,1601,410,11359,495,2448,591,17371,699,3654,819,
%U A063780 27487,954,4947,1099,42980,1260,6660,1436,59356,1628,8832,1836,82224,2061
%N A063780 a(n) is the number of pairs of integer quadruples (b_1, b_2, b_3, b_4) and (c_1, c_2, c_3, c_4) satisfying 1 <= b_1 < b_2 < b_3 < b_4 < n, 1 <= c_1 < c_2 < c_3 < c_4 < n, b_i != c_j for all i,j = 1,2,3,4 and Product_{i=1..4} cos(2*Pi*b_i/n) = Product_{i=1..4} cos(2*Pi*c_i/n).
%H A063780 Eckard Specht, <a href="/A063780/b063780.txt">Table of n, a(n) for n = 8..200</a>
%H A063780 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a063/A063780.java">Java program</a> (github)
%H A063780 Eckard Specht, <a href="/A063780/a063780.cpp.txt">C++ program</a>
%e A063780 For n=9, the only solution is (1, 4, 6, 7), (2, 3, 5, 8). - _Sean A. Irvine_, May 30 2023
%Y A063780 Cf. A063781.
%K A063780 nonn
%O A063780 8,3
%A A063780 _Eckard Specht_, Aug 17 2001
%E A063780 Revised by _Sean A. Irvine_, May 30 2023