A320129 -id:A320129 - cp's OEIS frontend

A320168 Number of ways to group the first 2*n positive integers into n pairs (xi, yi) with xi < yi, and such that the n numbers (yi mod xi) are all different.

1, 1, 2, 2, 7, 12, 22, 26, 85, 226, 717, 1695, 5071, 14275, 47405, 176747, 638329, 2166516

Offset: 0

Altug Alkan, Oct 07 2018

How does a(n+1)/a(n) behave as n increases?

			a(3) = 2 because {(1,3), (2,5), (4,6)} and {(1,5), (2,3), (4,6)} are corresponding sets.
a(4) = 7 because {(1,6), (2,5), (3,8), (4,7)}, {(1,3), (2,7), (4,6), (5,8)}, {(1,7), (2,3), (4,6), (5,8)}, {(1,3), (2,5), (4,7), (6,8)}, {(1,5), (2,3), (4,7), (6,8)}, {(1,2), (3,7), (4,6), (5,8)}, {(1,2), (3,8), (4,7), (5,6)} are corresponding sets.

David A. Corneth, Illustration for a(4)

Cf. A002968, A060963, A272363, A320129.

a(13)-a(17) from Rémy Sigrist, Oct 07 2018

A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.

Original entry on oeis.org

1, 9, 145, 4641, 231417, 16770369, 1671395713

Offset: 0

Altug Alkan, Oct 11 2018

It can be seen as interesting that a(t) = A178185(t+1) for 0 <= t <= 3.

			a(1) = 9 because {(1,4), (2,5), (3,6)}, {(1,5), (2,6), (3,4)}, {(1,6), (2,4), (3,5)}, {(1,3), (2,6), (4,5)}, {(1,5), (2,3), (4,6)}, {(1,6), (2,3), (4,5)}, {(1,3), (2,4), (5,6)}, {(1,2), (3,5), (4,6)}, {(1,2), (3,4), (5,6)} are corresponding sets.

Cf. A060963, A178185, A320129.

cp's OEIS Frontend

A320168 Number of ways to group the first 2*n positive integers into n pairs (xi, yi) with xi < yi, and such that the n numbers (yi mod xi) are all different.

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A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.

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cp's OEIS Frontend

A320168 Number of ways to group the first 2*n positive integers into n pairs (xi, yi) with xi < yi, and such that the n numbers (yi mod xi) are all different.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A320333 a(n) is the number of pairings of the first 2*k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2*n + 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.