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A275553
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Number of classes of endofunctions of [n] under vertical translation mod n, complement to n+1 and reversal.
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13
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1, 1, 2, 4, 24, 169, 2024, 29584, 525600, 10764961, 250030128, 6484436676, 185752964096, 5824523694025, 198428723433728, 7298231591777344, 288230377359679488, 12165297972404595841, 546477889989773968640, 26031837574639154232100, 1310720000002816000131072
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OFFSET
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0,3
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COMMENTS
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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).
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LINKS
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PROG
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(PARI) \\ see A056391 for Polya enumeration functions
a(n) = NonequivalentSorts(ReversiblePerms(n), DihedralPerms(n)); \\ Andrew Howroyd, Sep 30 2017
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CROSSREFS
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Cf. A000169 Classes under translation mod n
Cf. A168658 Classes under complement to n+1
Cf. A130293 Classes under translation and rotation
Cf. A081721 Classes under rotation and 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
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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