cp's OEIS Frontend

A275553 Number of classes of endofunctions of [n] under vertical translation mod n, complement to n+1 and reversal.

%I A275553 #7 Oct 01 2017 16:57:06
%S A275553 1,1,2,4,24,169,2024,29584,525600,10764961,250030128,6484436676,
%T A275553 185752964096,5824523694025,198428723433728,7298231591777344,
%U A275553 288230377359679488,12165297972404595841,546477889989773968640,26031837574639154232100,1310720000002816000131072
%N A275553 Number of classes of endofunctions of [n] under vertical translation mod n, complement to n+1 and reversal.
%C A275553 There are three size of classes : n, 2n, 4n.
%C A275553 n   c:n   c:2n   c:4n
%C A275553 ----------------------------------
%C A275553 0   1
%C A275553 1   1
%C A275553 2   2
%C A275553 3   1     2      1
%C A275553 4   4     10     10
%C A275553 5   1     24     144
%C A275553 6   8     148    1868
%C A275553 7   1     342    29241
%C A275553 For n odd, only the set of n constant functions can have a member of their class equal to their complement, so c:n size is 1.
%C A275553 For n even, we have 2^(n/2) binary words which have mirror-symmetry
%C A275553 There are three types of classes of size of 2n (stable by reversal, stable by complement, stable by rc as in A275550).
%H A275553 Andrew Howroyd, <a href="/A275553/b275553.txt">Table of n, a(n) for n = 0..100</a>
%o A275553 (PARI) \\ see A056391 for Polya enumeration functions
%o A275553 a(n) = NonequivalentSorts(ReversiblePerms(n), DihedralPerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275553 Cf. A000312 All endofunctions
%Y A275553 Cf. A000169 Classes under translation mod n
%Y A275553 Cf. A001700 Classes under sort
%Y A275553 Cf. A056665 Classes under rotation
%Y A275553 Cf. A168658 Classes under complement to n+1
%Y A275553 Cf. A130293 Classes under translation and rotation
%Y A275553 Cf. A081721 Classes under rotation and reversal
%Y A275553 Cf. A275549 Classes under reversal
%Y A275553 Cf. A275550 Classes under reversal and complement
%Y A275553 Cf. A275551 Classes under translation and reversal
%Y A275553 Cf. A275552 Classes under translation and complement
%Y A275553 Cf. A275554 Classes under translation, rotation and complement
%Y A275553 Cf. A275555 Classes under translation, rotation and reversal
%Y A275553 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275553 Cf. A275557 Classes under rotation and complement
%Y A275553 Cf. A275558 Classes under rotation, complement and reversal
%K A275553 nonn
%O A275553 0,3
%A A275553 _Olivier Gérard_, Aug 05 2016
%E A275553 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017