

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
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OFFSET

1,14


COMMENTS

a(n)=NPC(n;S;P) is the count of all neighborproperty cycles for a specific set S of n elements and a specific pairproperty P. For more details, see the link and A242519.
For this property P and sets {0,1,2,...,n1} 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 NeighborProperty 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



