A063780 - OEIS

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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).

0, 1, 3, 4, 9, 9, 18, 17, 93, 29, 84, 45, 433, 66, 253, 93, 1274, 126, 534, 166, 2940, 214, 1120, 270, 5866, 335, 1601, 410, 11359, 495, 2448, 591, 17371, 699, 3654, 819, 27487, 954, 4947, 1099, 42980, 1260, 6660, 1436, 59356, 1628, 8832, 1836, 82224, 2061

(list; graph; refs; listen; history; text; internal format)

OFFSET

8,3

LINKS

Eckard Specht, Table of n, a(n) for n = 8..200

Sean A. Irvine, Java program (github)

Eckard Specht, C++ program

EXAMPLE

For n=9, the only solution is (1, 4, 6, 7), (2, 3, 5, 8). - Sean A. Irvine, May 30 2023

CROSSREFS

Cf. A063781.

Sequence in context: A082188 A202499 A341319 * A307992 A323180 A095047