cp's OEIS Frontend

A275554 Number of classes of endofunctions of [n] under vertical translation mod n, rotation and complement to n+1.

%I A275554 #8 Oct 01 2017 16:57:51
%S A275554 1,1,2,3,14,65,680,8407,131416,2391515,50006040,1178973851,
%T A275554 30958827996,896080197025,28346960490560,973097534189967,
%U A275554 36028797169965112,1431211525754907905,60719765554419645244,2740193428892401092979,131072000000281600209176
%N A275554 Number of classes of endofunctions of [n] under vertical translation mod n, rotation and complement to n+1.
%C A275554 Because of the interaction between the two symmetries indexed by n, classes can be of size from n up to 2*n^2.
%C A275554 .
%C A275554 n  possible class sizes
%C A275554 -------------------------------
%C A275554 1  1
%C A275554 2  2
%C A275554 3  3, 6,                   18
%C A275554 4  4, 8,      16,          32
%C A275554 5  5, 10,                  50
%C A275554 6  6, 12, 18, 24,     36,  72
%C A275554 7  7, 14,                  98
%C A275554 .
%C A275554 but classes of size 2*n^2 account for the bulk of a(n).
%C A275554 n  number of classes
%C A275554 -----------------------------------
%C A275554 1  1
%C A275554 2  2
%C A275554 3  1, 1,                   1
%C A275554 4  2, 3,       4,          5
%C A275554 5  1, 2,                   62
%C A275554 6  2, 4,   2,  2,     48,  622
%C A275554 7  1, 3,                   8403
%H A275554 Andrew Howroyd, <a href="/A275554/b275554.txt">Table of n, a(n) for n = 0..100</a>
%o A275554 (PARI) \\ see A056391 for Polya enumeration functions
%o A275554 a(n) = NonequivalentSorts(CyclicPerms(n), DihedralPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275554 Cf. A000312 All endofunctions
%Y A275554 Cf. A000169 Classes under translation mod n
%Y A275554 Cf. A001700 Classes under sort
%Y A275554 Cf. A056665 Classes under rotation
%Y A275554 Cf. A168658 Classes under complement to n+1
%Y A275554 Cf. A130293 Classes under translation and rotation
%Y A275554 Cf. A081721 Classes under rotation and reversal
%Y A275554 Cf. A275549 Classes under reversal
%Y A275554 Cf. A275550 Classes under reversal and complement
%Y A275554 Cf. A275551 Classes under translation and reversal
%Y A275554 Cf. A275552 Classes under translation and complement
%Y A275554 Cf. A275553 Classes under translation, complement and reversal
%Y A275554 Cf. A275555 Classes under translation, rotation and reversal
%Y A275554 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275554 Cf. A275557 Classes under rotation and complement
%Y A275554 Cf. A275558 Classes under rotation, complement and reversal
%K A275554 nonn
%O A275554 0,3
%A A275554 _Olivier Gérard_, Aug 02 2016
%E A275554 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017