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 A275556 Number of classes of endofunctions of [n] under vertical translation mod n, rotation, complement to n+1 and reversal. 13
 1, 1, 2, 3, 13, 45, 412, 4375, 66988, 1199038, 25033020, 589567451, 15480284910, 448042511917, 14173510363424, 486548852524671, 18014399792942108, 715605766365332673, 30359882832309625502, 1370096714607544395379, 65536000002956800104588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Because of the interaction between the two symmetries indexed by n and the two involutions, classes can be of size from n up to 4*n^2. . n  possible class sizes ------------------------------------ 1  1 2  2 3  3, 6,                   18 4  4, 8,      16,          32,   64 5  5, 10,                  50,  100 6  6, 12, 18, 24,     36,  72,  144 7  7, 14,                  98,  196 . but classes of size 4*n^2 account for the bulk of a(n). n  number of classes ------------------------------------ 1  1 2  2 3  1, 1,                    1 4  2, 3,       4,           3,    1 5  1, 2,                   22,   20 6  2, 4,   2,  2,     28, 116,  258 7  1, 3,                  339, 4032 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 PROG (PARI) \\ see A056391 for Polya enumeration functions a(n) = NonequivalentSorts(DihedralPerms(n), DihedralPerms(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. A275557 Classes under rotation and complement Cf. A275558 Classes under rotation, complement and reversal Sequence in context: A226938 A301395 A206776 * A214888 A203985 A164511 Adjacent sequences:  A275553 A275554 A275555 * A275557 A275558 A275559 KEYWORD nonn AUTHOR Olivier Gérard, Aug 05 2016 EXTENSIONS Terms a(8) and beyond from Andrew Howroyd, Sep 30 2017 STATUS approved

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Last modified November 14 06:14 EST 2018. Contains 317162 sequences. (Running on oeis4.)