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A275555 Number of classes of endofunctions of [n] under vertical translation mod n, rotation and reversal. 13
1, 1, 2, 4, 16, 77, 730, 8578, 132422, 2394795, 50031012, 1179054376, 30959574248, 896082610429, 28346986843640, 973097619619654, 36028798243701780, 1431211529242786625, 60719765604009463866, 2740193429053744941868, 131072000002841600036024 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Because of the interaction between the two symmetries indexed by n, classes can be of size from n up to 2*n^2.
n possible class sizes
-----------------------------------
1 1
2 2
3 3, 6, 9
4 4, 8, 16, 32
5 5, 10, 25, 50
6 6, 12, 18, 24, 36, 72
7 7, 14, 49, 98
but classes of size 2*n^2 account for the bulk of a(n).
n number of classes
-----------------------------------
1 1
2 2
3 1, 1, 2
4 2, 3, 8, 3
5 1, 2, 24, 50
6 2, 4, 10, 2, 136, 576
7 1, 3, 342, 8232
LINKS
PROG
(PARI) \\ see A056391 for Polya enumeration functions
a(n) = NonequivalentSorts(DihedralPerms(n), CyclicPerms(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. 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: A155519 A180391 A371389 * A370485 A058926 A340900
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 March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)