A275554 - OEIS

%I #8 Oct 01 2017 16:57:51

%S 1,1,2,3,14,65,680,8407,131416,2391515,50006040,1178973851,

%T 30958827996,896080197025,28346960490560,973097534189967,

%U 36028797169965112,1431211525754907905,60719765554419645244,2740193428892401092979,131072000000281600209176

%N Number of classes of endofunctions of [n] under vertical translation mod n, rotation and complement to n+1.

%C Because of the interaction between the two symmetries indexed by n, classes can be of size from n up to 2*n^2.

%C .

%C n  possible class sizes

%C -------------------------------

%C 1  1

%C 2  2

%C 3  3, 6,                   18

%C 4  4, 8,      16,          32

%C 5  5, 10,                  50

%C 6  6, 12, 18, 24,     36,  72

%C 7  7, 14,                  98

%C .

%C but classes of size 2*n^2 account for the bulk of a(n).

%C n  number of classes

%C -----------------------------------

%C 1  1

%C 2  2

%C 3  1, 1,                   1

%C 4  2, 3,       4,          5

%C 5  1, 2,                   62

%C 6  2, 4,   2,  2,     48,  622

%C 7  1, 3,                   8403

%H Andrew Howroyd, <a href="/A275554/b275554.txt">Table of n, a(n) for n = 0..100</a>

%o (PARI) \\ see A056391 for Polya enumeration functions

%o a(n) = NonequivalentSorts(CyclicPerms(n), DihedralPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017

%Y Cf. A000312 All endofunctions

%Y Cf. A000169 Classes under translation mod n

%Y Cf. A001700 Classes under sort

%Y Cf. A056665 Classes under rotation

%Y Cf. A168658 Classes under complement to n+1

%Y Cf. A130293 Classes under translation and rotation

%Y Cf. A081721 Classes under rotation and reversal

%Y Cf. A275549 Classes under reversal

%Y Cf. A275550 Classes under reversal and complement

%Y Cf. A275551 Classes under translation and reversal

%Y Cf. A275552 Classes under translation and complement

%Y Cf. A275553 Classes under translation, complement and reversal

%Y Cf. A275555 Classes under translation, rotation and reversal

%Y Cf. A275556 Classes under translation, rotation, complement and reversal

%Y Cf. A275557 Classes under rotation and complement

%Y Cf. A275558 Classes under rotation, complement and reversal

%K nonn

%O 0,3

%A _Olivier Gérard_, Aug 02 2016

%E Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017