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A275556 Number of classes of endofunctions of [n] under vertical translation mod n, rotation, complement to n+1 and reversal. 13
1, 1, 2, 3, 13, 45, 412, 4375, 66988, 1199038, 25033020, 589567451, 15480284910, 448042511917, 14173510363424, 486548852524671, 18014399792942108, 715605766365332673, 30359882832309625502, 1370096714607544395379, 65536000002956800104588 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A226938 A301395 A206776 * A214888 A203985 A164511

Adjacent sequences:  A275553 A275554 A275555 * A275557 A275558 A275559

KEYWORD

nonn

AUTHOR

Olivier Gérard, Aug 05 2016

EXTENSIONS

Terms a(8) and beyond from Andrew Howroyd, Sep 30 2017

STATUS

approved

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Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)