

A118537


Number of functions f: {1, 2, ..., n} > {1, 2, ..., n} such that f(1) != f(2), f(2) != f(3), ..., f(n1) != f(n), f(n) != f(1).


4



2, 6, 84, 1020, 15630, 279930, 5764808, 134217720, 3486784410, 99999999990, 3138428376732, 106993205379060, 3937376385699302, 155568095557812210, 6568408355712890640, 295147905179352825840, 14063084452067724991026
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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
a(n) is also the number of graph colorings of the cycle graph C_n with n colors.  Orson R. L. Peters, Jul 27 2020


LINKS

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


FORMULA

a(n) = (n1)^n + (1)^n*(n1).


MATHEMATICA

a[n_]:=(n1)^n + (1)^n*(n1); Array[a, 50, {2, 51}] (* Stefano Spezia, Sep 07 2018 *)


PROG

(PARI) a(n) = (n1)^n + (1)^n*(n1); \\ Andrew Howroyd, Sep 05 2018
(MAGMA) [(n1)^n + (1)^n*(n1) : n in [2..20]]; // Wesley Ivan Hurt, Jul 27 2020


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



