OFFSET
0,3
COMMENTS
Because of the interaction between the two symmetries indexed by n and the two involutions, classes can be of size from n up to 4*n^2.
.
n possible class sizes
------------------------------------
1 1
2 2
3 3, 6, 18
4 4, 8, 16, 32, 64
5 5, 10, 50, 100
6 6, 12, 18, 24, 36, 72, 144
7 7, 14, 98, 196
.
but classes of size 4*n^2 account for the bulk of a(n).
n number of classes
------------------------------------
1 1
2 2
3 1, 1, 1
4 2, 3, 4, 3, 1
5 1, 2, 22, 20
6 2, 4, 2, 2, 28, 116, 258
7 1, 3, 339, 4032
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
PROG
(PARI) \\ see A056391 for Polya enumeration functions
a(n) = NonequivalentSorts(DihedralPerms(n), DihedralPerms(n)); \\ Andrew Howroyd, Sep 30 2017
CROSSREFS
Cf. A000312 All endofunctions
Cf. A000169 Classes under translation mod n
Cf. A001700 Classes under sort
Cf. A056665 Classes under rotation
Cf. A168658 Classes under complement to n+1
Cf. A130293 Classes under translation and rotation
Cf. A081721 Classes under rotation and reversal
Cf. A275549 Classes under reversal
Cf. A275550 Classes under reversal and complement
Cf. A275551 Classes under translation and reversal
Cf. A275552 Classes under translation and complement
Cf. A275553 Classes under translation, complement and reversal
Cf. A275554 Classes under translation, rotation and complement
Cf. A275555 Classes under translation, rotation and reversal
Cf. A275557 Classes under rotation and complement
Cf. A275558 Classes under rotation, complement and reversal
KEYWORD
nonn
AUTHOR
Olivier Gérard, Aug 05 2016
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, Sep 30 2017
STATUS
approved