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 A275558 Number of classes of endofunctions of [n] under rotation, complement to n+1 and reversal. 15
 1, 1, 2, 6, 31, 195, 2182, 30100, 529674, 10778125, 250155012, 6484839306, 185757443582, 5824538174455, 198428907905336, 7298232189810696, 288230385949610020, 12165298000307625609, 546477890436083284338, 26031837576091248872110, 1310720000028416000168044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Classes can be of size 1,2,4, n, 2n or 4n. . n   1  2  4      n     2n     4n --------------------------------- 1   1 2   0  2 3   1  1                4 4   0  4  4      0     17      6 5   1  2  0      0     72    120 6   0  6  6     30    410   1730 7   1  3  0      0   1368  28728 . For n odd, the constant function (n+1)/2 is the only stable by rotation, complement and reversal. 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(DihedralPerms(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. A275557 Classes under rotation and complement Sequence in context: A287592 A054141 A007710 * A094639 A113719 A018225 Adjacent sequences:  A275555 A275556 A275557 * A275559 A275560 A275561 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 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)