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A275555 Number of classes of endofunctions of [n] under vertical translation mod n, rotation and reversal.

%I A275555 #9 Oct 01 2017 16:59:24
%S A275555 1,1,2,4,16,77,730,8578,132422,2394795,50031012,1179054376,
%T A275555 30959574248,896082610429,28346986843640,973097619619654,
%U A275555 36028798243701780,1431211529242786625,60719765604009463866,2740193429053744941868,131072000002841600036024
%N A275555 Number of classes of endofunctions of [n] under vertical translation mod n, rotation and reversal.
%C A275555 Because of the interaction between the two symmetries indexed by n, classes can be of size from n up to 2*n^2.
%C A275555 n  possible class sizes
%C A275555 -----------------------------------
%C A275555 1  1
%C A275555 2  2
%C A275555 3  3, 6,   9
%C A275555 4  4, 8,      16,               32
%C A275555 5  5, 10,         25,           50
%C A275555 6  6, 12, 18, 24,     36,       72
%C A275555 7  7, 14,                 49,   98
%C A275555 but classes of size 2*n^2 account for the bulk of a(n).
%C A275555 n  number of classes
%C A275555 -----------------------------------
%C A275555 1  1
%C A275555 2  2
%C A275555 3  1, 1,   2
%C A275555 4  2, 3,       8,               3
%C A275555 5  1, 2,          24,           50
%C A275555 6  2, 4,  10,  2,    136,       576
%C A275555 7  1, 3,                 342,   8232
%H A275555 Andrew Howroyd, <a href="/A275555/b275555.txt">Table of n, a(n) for n = 0..100</a>
%o A275555 (PARI) \\ see A056391 for Polya enumeration functions
%o A275555 a(n) = NonequivalentSorts(DihedralPerms(n), CyclicPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275555 Cf. A000312 All endofunctions
%Y A275555 Cf. A000169 Classes under translation mod n
%Y A275555 Cf. A001700 Classes under sort
%Y A275555 Cf. A056665 Classes under rotation
%Y A275555 Cf. A168658 Classes under complement to n+1
%Y A275555 Cf. A130293 Classes under translation and rotation
%Y A275555 Cf. A081721 Classes under rotation and reversal
%Y A275555 Cf. A275549 Classes under reversal
%Y A275555 Cf. A275550 Classes under reversal and complement
%Y A275555 Cf. A275551 Classes under translation and reversal
%Y A275555 Cf. A275552 Classes under translation and complement
%Y A275555 Cf. A275553 Classes under translation, complement and reversal
%Y A275555 Cf. A275554 Classes under translation, rotation and complement
%Y A275555 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275555 Cf. A275557 Classes under rotation and complement
%Y A275555 Cf. A275558 Classes under rotation, complement and reversal
%K A275555 nonn
%O A275555 0,3
%A A275555 _Olivier Gérard_, Aug 05 2016
%E A275555 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017