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A118537 Number of functions f: {1, 2, ..., n} --> {1, 2, ..., n} such that f(1) != f(2), f(2) != f(3), ..., f(n-1) != f(n), f(n) != f(1). 4
2, 6, 84, 1020, 15630, 279930, 5764808, 134217720, 3486784410, 99999999990, 3138428376732, 106993205379060, 3937376385699302, 155568095557812210, 6568408355712890640, 295147905179352825840, 14063084452067724991026 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) is also the number of circuits of length n in the complete graph on n vertices. - Thibaut Lienart (syncthib(AT)gmail.com), Jan 29 2010

Circuits are allowed to be self intersecting and are directional with a designated start node. The number of (self avoiding) directed cycles is given by A124355. - Andrew Howroyd, Sep 05 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 2..100

FORMULA

a(n) = (n-1)^n + (-1)^n*(n-1).

MATHEMATICA

a[n_]:=(n-1)^n + (-1)^n*(n-1); Array[a, 50, {2, 51}] (* Stefano Spezia, Sep 07 2018 *)

PROG

(PARI) a(n) = (n-1)^n + (-1)^n*(n-1); \\ Andrew Howroyd, Sep 05 2018

CROSSREFS

Cf. A055897, A124355.

Sequence in context: A245463 A325949 A055706 * A109892 A268534 A055702

Adjacent sequences:  A118534 A118535 A118536 * A118538 A118539 A118540

KEYWORD

nonn

AUTHOR

Warut Roonguthai, May 06 2006

STATUS

approved

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Last modified October 23 12:53 EDT 2019. Contains 328345 sequences. (Running on oeis4.)