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%I #9 Oct 01 2017 17:02:02
%S 1,1,2,6,31,195,2182,30100,529674,10778125,250155012,6484839306,
%T 185757443582,5824538174455,198428907905336,7298232189810696,
%U 288230385949610020,12165298000307625609,546477890436083284338,26031837576091248872110,1310720000028416000168044
%N Number of classes of endofunctions of [n] under rotation, complement to n+1 and reversal.
%C Classes can be of size 1,2,4, n, 2n or 4n.
%C .
%C n 1 2 4 n 2n 4n
%C ---------------------------------
%C 1 1
%C 2 0 2
%C 3 1 1 4
%C 4 0 4 4 0 17 6
%C 5 1 2 0 0 72 120
%C 6 0 6 6 30 410 1730
%C 7 1 3 0 0 1368 28728
%C .
%C For n odd, the constant function (n+1)/2 is the only stable by rotation, complement and reversal. So #c1=1.
%C 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 Andrew Howroyd, <a href="/A275558/b275558.txt">Table of n, a(n) for n = 0..100</a>
%o (PARI) \\ see A056391 for Polya enumeration functions
%o a(n) = NonequivalentSorts(DihedralPerms(n), ReversiblePerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y Cf. A000312 All endofunctions
%Y Cf. A000169 Classes under translation mod n
%Y Cf. A001700 Classes under sort
%Y Cf. A056665 Classes under rotation
%Y Cf. A168658 Classes under complement to n+1
%Y Cf. A130293 Classes under translation and rotation
%Y Cf. A081721 Classes under rotation and reversal
%Y Cf. A275549 Classes under reversal
%Y Cf. A275550 Classes under reversal and complement
%Y Cf. A275551 Classes under translation and reversal
%Y Cf. A275552 Classes under translation and complement
%Y Cf. A275553 Classes under translation, complement and reversal
%Y Cf. A275554 Classes under translation, rotation and complement
%Y Cf. A275555 Classes under translation, rotation and reversal
%Y Cf. A275556 Classes under translation, rotation, complement and reversal
%Y Cf. A275557 Classes under rotation and complement
%K nonn
%O 0,3
%A _Olivier Gérard_, Aug 05 2016
%E Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017
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