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 A275553 Number of classes of endofunctions of [n] under vertical translation mod n, complement to n+1 and reversal. 13
 1, 1, 2, 4, 24, 169, 2024, 29584, 525600, 10764961, 250030128, 6484436676, 185752964096, 5824523694025, 198428723433728, 7298231591777344, 288230377359679488, 12165297972404595841, 546477889989773968640, 26031837574639154232100, 1310720000002816000131072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS There are three size of classes : n, 2n, 4n. n   c:n   c:2n   c:4n ---------------------------------- 0   1 1   1 2   2 3   1     2      1 4   4     10     10 5   1     24     144 6   8     148    1868 7   1     342    29241 For n odd, only the set of n constant functions can have a member of their class equal to their complement, so c:n size is 1. For n even, we have 2^(n/2) binary words which have mirror-symmetry There are three types of classes of size of 2n (stable by reversal, stable by complement, stable by rc as in A275550). LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 PROG (PARI) \\ see A056391 for Polya enumeration functions a(n) = NonequivalentSorts(ReversiblePerms(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. 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. A275557 Classes under rotation and complement Cf. A275558 Classes under rotation, complement and reversal Sequence in context: A002875 A110491 A019010 * A009672 A018988 A012587 Adjacent sequences:  A275550 A275551 A275552 * A275554 A275555 A275556 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 January 23 08:58 EST 2019. Contains 319376 sequences. (Running on oeis4.)