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A063781 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} sin(2*Pi*b_i/n) = Product_{i=1..4} sin(2*Pi*c_i/n).

%I A063781 #14 May 30 2023 23:13:26
%S A063781 0,1,3,4,5,9,18,17,41,29,84,45,167,66,253,93,386,126,534,166,782,214,
%T A063781 966,270,1380,335,1601,410,3053,495,2448,591,3135,699,3546,819,4785,
%U A063781 952,4947,1099,8350,1260,6660,1436,8804,1628,8724,1836,10620,2061,11191
%N A063781 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} sin(2*Pi*b_i/n) = Product_{i=1..4} sin(2*Pi*c_i/n).
%H A063781 Eckard Specht, <a href="/A063781/b063781.txt">Table of n, a(n) for n = 8..200</a>
%e A063781 For n=9, the only solution is (1, 4, 6, 7), (2, 3, 5, 8). - _Sean A. Irvine_, May 30 2023
%Y A063781 Cf. A063780.
%K A063781 nonn
%O A063781 8,3
%A A063781 _Eckard Specht_, Aug 17 2001
%E A063781 Revised by _Sean A. Irvine_, May 30 2023