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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n)=NPC(2n;S;P) is the count of all neighbor-property cycles for a specific set S of 2n elements and a specific pair-property 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 Neighbor-Property 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

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Last modified July 25 20:38 EDT 2017. Contains 289797 sequences.