cp's OEIS Frontend

A275556 Number of classes of endofunctions of [n] under vertical translation mod n, rotation, complement to n+1 and reversal.

%I A275556 #7 Oct 01 2017 17:01:16
%S A275556 1,1,2,3,13,45,412,4375,66988,1199038,25033020,589567451,15480284910,
%T A275556 448042511917,14173510363424,486548852524671,18014399792942108,
%U A275556 715605766365332673,30359882832309625502,1370096714607544395379,65536000002956800104588
%N A275556 Number of classes of endofunctions of [n] under vertical translation mod n, rotation, complement to n+1 and reversal.
%C A275556 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 A275556 .
%C A275556 n  possible class sizes
%C A275556 ------------------------------------
%C A275556 1  1
%C A275556 2  2
%C A275556 3  3, 6,                   18
%C A275556 4  4, 8,      16,          32,   64
%C A275556 5  5, 10,                  50,  100
%C A275556 6  6, 12, 18, 24,     36,  72,  144
%C A275556 7  7, 14,                  98,  196
%C A275556 .
%C A275556 but classes of size 4*n^2 account for the bulk of a(n).
%C A275556 n  number of classes
%C A275556 ------------------------------------
%C A275556 1  1
%C A275556 2  2
%C A275556 3  1, 1,                    1
%C A275556 4  2, 3,       4,           3,    1
%C A275556 5  1, 2,                   22,   20
%C A275556 6  2, 4,   2,  2,     28, 116,  258
%C A275556 7  1, 3,                  339, 4032
%H A275556 Andrew Howroyd, <a href="/A275556/b275556.txt">Table of n, a(n) for n = 0..100</a>
%o A275556 (PARI) \\ see A056391 for Polya enumeration functions
%o A275556 a(n) = NonequivalentSorts(DihedralPerms(n), DihedralPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275556 Cf. A000312 All endofunctions
%Y A275556 Cf. A000169 Classes under translation mod n
%Y A275556 Cf. A001700 Classes under sort
%Y A275556 Cf. A056665 Classes under rotation
%Y A275556 Cf. A168658 Classes under complement to n+1
%Y A275556 Cf. A130293 Classes under translation and rotation
%Y A275556 Cf. A081721 Classes under rotation and reversal
%Y A275556 Cf. A275549 Classes under reversal
%Y A275556 Cf. A275550 Classes under reversal and complement
%Y A275556 Cf. A275551 Classes under translation and reversal
%Y A275556 Cf. A275552 Classes under translation and complement
%Y A275556 Cf. A275553 Classes under translation, complement and reversal
%Y A275556 Cf. A275554 Classes under translation, rotation and complement
%Y A275556 Cf. A275555 Classes under translation, rotation and reversal
%Y A275556 Cf. A275557 Classes under rotation and complement
%Y A275556 Cf. A275558 Classes under rotation, complement and reversal
%K A275556 nonn
%O A275556 0,3
%A A275556 _Olivier Gérard_, Aug 05 2016
%E A275556 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017