A275557 - OEIS

%I #8 Oct 01 2017 16:51:42

%S 1,1,2,6,38,315,3932,58828,1049108,21523445,500010024,12968712306,

%T 371504436220,11649042561247,396857394156656,14596463012746392,

%U 576460752571867208,24330595937833434249,1092955779880370116836,52063675148955620766430,2621440000000512000336088

%N Number of classes of endofunctions of [n] under rotation and complement to n+1.

%C Classes can be of size 1,2,4, n and 2n.

%C n   1  2  4      n     2n

%C --------------------------

%C 1   1

%C 2   0  2

%C 3   1  1                4

%C 4   0  4  4      2     28

%C 5   1  2  0      0    312

%C 6   0  6  6     70   3850

%C 7   1  3  0      0  58824

%C For n odd, the constant function (n+1)/2 is the only stable by rotation and complement. 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="/A275557/b275557.txt">Table of n, a(n) for n = 0..100</a>

%o (PARI) \\ see A056391 for Polya enumeration functions

%o a(n) = NonequivalentSorts(CyclicPerms(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. A275558 Classes under rotation, complement and reversal

%K nonn

%O 0,3

%A _Olivier Gérard_, Aug 05 2016

%E Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017