

A242533


Number of cyclic arrangements of S={1,2,...,2n} such that the difference of any two neighbors is coprime to their sum.


15



1, 1, 2, 36, 288, 3888, 200448, 4257792, 139511808, 11813990400, 532754620416
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OFFSET

1,3


COMMENTS

a(n)=NPC(2n;S;P) is the count of all neighborproperty cycles for a specific set S of 2n elements and a specific pairproperty P. For more details, see the link and A242519.
Conjecture: in this case it seems that NPC(n;S;P)=0 for all odd n, so only the even ones are listed. This is definitely not the case when the property P is replaced by its negation (see A242534).


LINKS

Table of n, a(n) for n=1..11.
S. Sykora, On NeighborProperty Cycles, Stan's Library, Volume V, 2014.


EXAMPLE

For n=4, the only cycle is {1,2,3,4}.
The two solutions for n=6 are: C_1={1,2,3,4,5,6} and C_2={1,4,3,2,5,6}.


PROG

(C++) See the link.


CROSSREFS

Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242531, A242532, A242534.
Sequence in context: A099903 A074426 A082636 * A273325 A035603 A126735
Adjacent sequences: A242530 A242531 A242532 * A242534 A242535 A242536


KEYWORD

nonn,hard,more


AUTHOR

Stanislav Sykora, May 30 2014


EXTENSIONS

a(10)a(11) from Fausto A. C. Cariboni, May 31 2017, Jun 01 2017


STATUS

approved



