cp's OEIS Frontend

A275557 Number of classes of endofunctions of [n] under rotation and complement to n+1.

%I A275557 #8 Oct 01 2017 16:51:42
%S A275557 1,1,2,6,38,315,3932,58828,1049108,21523445,500010024,12968712306,
%T A275557 371504436220,11649042561247,396857394156656,14596463012746392,
%U A275557 576460752571867208,24330595937833434249,1092955779880370116836,52063675148955620766430,2621440000000512000336088
%N A275557 Number of classes of endofunctions of [n] under rotation and complement to n+1.
%C A275557 Classes can be of size 1,2,4, n and 2n.
%C A275557 n   1  2  4      n     2n
%C A275557 --------------------------
%C A275557 1   1
%C A275557 2   0  2
%C A275557 3   1  1                4
%C A275557 4   0  4  4      2     28
%C A275557 5   1  2  0      0    312
%C A275557 6   0  6  6     70   3850
%C A275557 7   1  3  0      0  58824
%C A275557 For n odd, the constant function (n+1)/2 is the only stable by rotation and complement. So #c1=1.
%C A275557 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 A275557 Andrew Howroyd, <a href="/A275557/b275557.txt">Table of n, a(n) for n = 0..100</a>
%o A275557 (PARI) \\ see A056391 for Polya enumeration functions
%o A275557 a(n) = NonequivalentSorts(CyclicPerms(n), ReversiblePerms(n)); \\ _Andrew Howroyd_, Sep 30 2017
%Y A275557 Cf. A000312 All endofunctions
%Y A275557 Cf. A000169 Classes under translation mod n
%Y A275557 Cf. A001700 Classes under sort
%Y A275557 Cf. A056665 Classes under rotation
%Y A275557 Cf. A168658 Classes under complement to n+1
%Y A275557 Cf. A130293 Classes under translation and rotation
%Y A275557 Cf. A081721 Classes under rotation and reversal
%Y A275557 Cf. A275549 Classes under reversal
%Y A275557 Cf. A275550 Classes under reversal and complement
%Y A275557 Cf. A275551 Classes under translation and reversal
%Y A275557 Cf. A275552 Classes under translation and complement
%Y A275557 Cf. A275553 Classes under translation, complement and reversal
%Y A275557 Cf. A275554 Classes under translation, rotation and complement
%Y A275557 Cf. A275555 Classes under translation, rotation and reversal
%Y A275557 Cf. A275556 Classes under translation, rotation, complement and reversal
%Y A275557 Cf. A275558 Classes under rotation, complement and reversal
%K A275557 nonn
%O A275557 0,3
%A A275557 _Olivier Gérard_, Aug 05 2016
%E A275557 Terms a(8) and beyond from _Andrew Howroyd_, Sep 30 2017