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%I #7 Oct 01 2017 17:01:16
%S 1,1,2,3,13,45,412,4375,66988,1199038,25033020,589567451,15480284910,
%T 448042511917,14173510363424,486548852524671,18014399792942108,
%U 715605766365332673,30359882832309625502,1370096714607544395379,65536000002956800104588
%N Number of classes of endofunctions of [n] under vertical translation mod n, rotation, complement to n+1 and reversal.
%C 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.
%C .
%C n possible class sizes
%C ------------------------------------
%C 1 1
%C 2 2
%C 3 3, 6, 18
%C 4 4, 8, 16, 32, 64
%C 5 5, 10, 50, 100
%C 6 6, 12, 18, 24, 36, 72, 144
%C 7 7, 14, 98, 196
%C .
%C but classes of size 4*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, 3, 1
%C 5 1, 2, 22, 20
%C 6 2, 4, 2, 2, 28, 116, 258
%C 7 1, 3, 339, 4032
%H Andrew Howroyd, <a href="/A275556/b275556.txt">Table of n, a(n) for n = 0..100</a>
%o (PARI) \\ see A056391 for Polya enumeration functions
%o a(n) = NonequivalentSorts(DihedralPerms(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. A275554 Classes under translation, rotation and complement
%Y Cf. A275555 Classes under translation, rotation 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 05 2016
%E Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017
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