This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A275557 Number of classes of endofunctions of [n] under rotation and complement to n+1. 13
 1, 1, 2, 6, 38, 315, 3932, 58828, 1049108, 21523445, 500010024, 12968712306, 371504436220, 11649042561247, 396857394156656, 14596463012746392, 576460752571867208, 24330595937833434249, 1092955779880370116836, 52063675148955620766430, 2621440000000512000336088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Classes can be of size 1,2,4, n and 2n. n   1  2  4      n     2n -------------------------- 1   1 2   0  2 3   1  1                4 4   0  4  4      2     28 5   1  2  0      0    312 6   0  6  6     70   3850 7   1  3  0      0  58824 For n odd, the constant function (n+1)/2 is the only stable by rotation and complement. So #c1=1. 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. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 PROG (PARI) \\ see A056391 for Polya enumeration functions a(n) = NonequivalentSorts(CyclicPerms(n), ReversiblePerms(n)); \\ Andrew Howroyd, Sep 30 2017 CROSSREFS Cf. A000312 All endofunctions Cf. A000169 Classes under translation mod n Cf. A001700 Classes under sort Cf. A056665 Classes under rotation Cf. A168658 Classes under complement to n+1 Cf. A130293 Classes under translation and rotation Cf. A081721 Classes under rotation and reversal Cf. A275549 Classes under reversal Cf. A275550 Classes under reversal and complement Cf. A275551 Classes under translation and reversal Cf. A275552 Classes under translation and complement Cf. A275553 Classes under translation, complement and reversal Cf. A275554 Classes under translation, rotation and complement Cf. A275555 Classes under translation, rotation and reversal Cf. A275556 Classes under translation, rotation, complement and reversal Cf. A275558 Classes under rotation, complement and reversal Sequence in context: A085447 A078673 A052841 * A197972 A068184 A067106 Adjacent sequences:  A275554 A275555 A275556 * A275558 A275559 A275560 KEYWORD nonn AUTHOR Olivier Gérard, Aug 05 2016 EXTENSIONS Terms a(8) and beyond from Andrew Howroyd, Sep 30 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)