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A242532 Number of cyclic arrangements of S={2,3,...,n+1} such that the difference of any two neighbors is greater than 1, and a divisor of their sum. 15
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, 39, 0, 0, 0, 0, 319, 967, 0, 0, 1464, 6114, 16856, 44370, 0, 0, 0, 0, 2032951, 8840796, 12791922, 101519154, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

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.

For this property P and sets {0,1,2,...,n-1} or {1,2,...,n} the problem does not appear to have any solution.

a(40)=a(41)=a(42)=a(43)=a(46)=a(47)=0. - Fausto A. C. Cariboni, May 17 2017

LINKS

Table of n, a(n) for n=1..37.

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

EXAMPLE

The shortest such cycle is of length n=9: {2,4,8,10,5,7,9,3,6}.

The next a(n)>0 occurs for n=14 and has 20 solutions.

The first and the last of these are:

C_1={2,4,8,10,5,7,14,12,15,13,11,9,3,6},

C_2={2,4,12,15,13,11,9,3,5,7,14,10,8,6}.

PROG

(C++) See the link.

CROSSREFS

Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242531, A242533, A242534.

Sequence in context: A259734 A217427 A165442 * A132606 A054288 A238245

Adjacent sequences:  A242529 A242530 A242531 * A242533 A242534 A242535

KEYWORD

nonn,hard,more

AUTHOR

Stanislav Sykora, May 30 2014

EXTENSIONS

a(29)-a(37) from Fausto A. C. Cariboni, May 17 2017

STATUS

approved

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Last modified June 23 18:19 EDT 2017. Contains 288668 sequences.