A357442 Consider a clock face with 2*n "hours" marked around the dial; a(n) = number of ways to match the even hours to the odd hours, modulo rotations and reflections.

1, 1, 3, 5, 17, 53, 260, 1466, 10915, 93196, 917898, 10015299, 119914982, 1557364352, 21797494987, 326930305166, 5230756117008, 88922108947567, 1600594738591550, 30411281088326498, 608225534389576956, 12772735698577492558

Offset

1,3

Links

Table of n, a(n) for n=1..22.

Barry Cipra, Illustration for a(5) = 17

N. J. A. Sloane, Sketch illustrating a(1) = a(2) = 1, a(3) = 3

Philip Todd, Theorem Discovery Amongst Cyclic Polygons, arXiv:2401.13002 [cs.CG], 2024.

Formula

See PARI code for the formula. - Max Alekseyev, Nov 10 2022

Prog

(PARI) { a357442(n) = ( sumdiv(n, d, (n\d)!*d^(n\d)*eulerphi(d)) + n*sum(k=0, n\2, n!\k!\2^k\(n-2*k)!) + if(n%2, n*((n-1)\2)!*2^((n-1)\2) + sumdiv(n, d, eulerphi(d)*sum(k=0, n\d\2, (n\d)! \ (2*k+1)! \ ((n\d-1)\2-k)! * (d/2)^((n\d-1)\2-k) ))) )\n\4; } \\ Max Alekseyev, Nov 10 2022

Crossrefs

Cf. A000031, A000699, A007769, A059375.

Sequence in context: A006483 A177960 A271659 * A049540 A097144 A219108

Adjacent sequences: A357439 A357440 A357441 * A357443 A357444 A357445

Keyword

nonn

Author

N. J. A. Sloane, Nov 06 2022, based on an email from Barry Cipra, Oct 26 2022

Extensions

Terms a(7) onward from Max Alekseyev, Nov 10 2022

Status

approved