A063781 -id:A063781 - cp's OEIS frontend

A063779 Duplicate of A063781.

15, 18, 20, 24, 25, 30, 33, 35, 36, 40, 42, 45, 48, 50, 54, 55, 57, 60, 63, 65, 66, 70, 72, 75, 78, 80, 84, 85, 90, 95, 96, 99, 100, 102, 105, 106, 108, 109, 110, 114, 115, 118, 120, 125, 126, 128, 129, 130, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143

Offset: 1

dead

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(2Pib_i/n) = Product_{i=1..4} cos(2Pic_i/n).

Original entry on oeis.org

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

Offset: 8

Eckard Specht, Aug 17 2001

nonn

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

Eckard Specht, Table of n, a(n) for n = 8..200
Sean A. Irvine, Java program (github)
Eckard Specht, C++ program

Cf. A063781.

Revised by Sean A. Irvine, May 30 2023

cp's OEIS Frontend

A063779 Duplicate of A063781.

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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(2Pib_i/n) = Product_{i=1..4} cos(2Pic_i/n).

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cp's OEIS Frontend

A063779 Duplicate of A063781.

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Author

Keywords

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).

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Extensions

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(2Pib_i/n) = Product_{i=1..4} cos(2Pic_i/n).