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A242534 Number of cyclic arrangements of S={1,2,...,n} such that the difference of any two neighbors is not coprime to their sum. 16
1, 0, 0, 0, 0, 0, 0, 0, 0, 72, 288, 3600, 17856, 174528, 2540160, 14768640, 101030400, 1458266112, 11316188160, 140951577600, 2659218508800, 30255151463424, 287496736542720, 5064092578713600, 76356431941939200, 987682437203558400, 19323690313219522560 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

a(n)=NPC(n;S;P) is the count of all neighbor-property cycles for a specific set S of n elements and a specific pair-property P. For more details, see the link and A242519.

Compare this with A242533 where the property is inverted.

LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..27

S. Sykora, On Neighbor-Property Cycles, Stan's Library, Volume V, 2014.

EXAMPLE

The first and the last of the 72 cycles for n=10 are:

C_1={1,3,5,10,2,4,8,6,9,7} and C_72={1,7,5,10,8,4,2,6,3,9}.

There are no solutions for cycle lengths from 2 to 9.

PROG

(C++) See the link.

CROSSREFS

Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242531, A242532, A242533.

Sequence in context: A004007 A279272 A173546 * A277430 A277991 A205627

Adjacent sequences:  A242531 A242532 A242533 * A242535 A242536 A242537

KEYWORD

nonn,hard

AUTHOR

Stanislav Sykora, May 30 2014

EXTENSIONS

a(19)-a(27) from Hiroaki Yamanouchi, Aug 30 2014

STATUS

approved

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Last modified May 26 03:13 EDT 2017. Contains 287073 sequences.