cp's OEIS Frontend

A275558 Number of classes of endofunctions of [n] under rotation, complement to n+1 and reversal.

%I A275558 #9 Oct 01 2017 17:02:02
%S A275558 1,1,2,6,31,195,2182,30100,529674,10778125,250155012,6484839306,
%T A275558 185757443582,5824538174455,198428907905336,7298232189810696,
%U A275558 288230385949610020,12165298000307625609,546477890436083284338,26031837576091248872110,1310720000028416000168044
%N A275558 Number of classes of endofunctions of [n] under rotation, complement to n+1 and reversal.
%C A275558 Classes can be of size 1,2,4, n, 2n or 4n.
%C A275558 .
%C A275558 n   1  2  4      n     2n     4n
%C A275558 ---------------------------------
%C A275558 1   1
%C A275558 2   0  2
%C A275558 3   1  1                4
%C A275558 4   0  4  4      0     17      6
%C A275558 5   1  2  0      0     72    120
%C A275558 6   0  6  6     30    410   1730
%C A275558 7   1  3  0      0   1368  28728
%C A275558 .
%C A275558 For n odd, the constant function (n+1)/2 is the only stable by rotation, complement and reversal. So #c1=1.
%C A275558 For n even, there is no stable function, so #c1=0, but constant functions are grouped two by two making n/2 classes of size 2. Functions alternating a value and its complement are also grouped two by two, making another n/2 classes. This gives #c2=n.
%H A275558 Andrew Howroyd, <a href="/A275558/b275558.txt">Table of n, a(n) for n = 0..100</a>
%o A275558 (PARI) \\ see A056391 for Polya enumeration functions
%o A275558 a(n) = NonequivalentSorts(DihedralPerms(n), ReversiblePerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275558 Cf. A000312 All endofunctions
%Y A275558 Cf. A000169 Classes under translation mod n
%Y A275558 Cf. A001700 Classes under sort
%Y A275558 Cf. A056665 Classes under rotation
%Y A275558 Cf. A168658 Classes under complement to n+1
%Y A275558 Cf. A130293 Classes under translation and rotation
%Y A275558 Cf. A081721 Classes under rotation and reversal
%Y A275558 Cf. A275549 Classes under reversal
%Y A275558 Cf. A275550 Classes under reversal and complement
%Y A275558 Cf. A275551 Classes under translation and reversal
%Y A275558 Cf. A275552 Classes under translation and complement
%Y A275558 Cf. A275553 Classes under translation, complement and reversal
%Y A275558 Cf. A275554 Classes under translation, rotation and complement
%Y A275558 Cf. A275555 Classes under translation, rotation and reversal
%Y A275558 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275558 Cf. A275557 Classes under rotation and complement
%K A275558 nonn
%O A275558 0,3
%A A275558 _Olivier Gérard_, Aug 05 2016
%E A275558 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017