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A242531 Number of cyclic arrangements of S={1,2,...,n} such that the difference of any two neighbors is a divisor of their sum. 15
0, 1, 1, 1, 1, 4, 3, 9, 26, 82, 46, 397, 283, 1675, 9938, 19503, 10247, 97978, 70478, 529383, 3171795, 7642285, 3824927, 48091810, 116017829, 448707198, 1709474581, 6445720883 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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.

LINKS

Table of n, a(n) for n=1..28.

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

EXAMPLE

The only such cycle of length n=5 is {1,2,4,5,3}.

For n=7 there are three solutions: C_1={1,2,4,5,7,6,3}, C_2={1,2,4,6,7,5,3}, C_3={1,2,6,7,5,4,3}.

PROG

(C++) See the link.

CROSSREFS

Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242532, A242533, A242534.

Sequence in context: A103218 A107381 A062882 * A275160 A132192 A147756

Adjacent sequences:  A242528 A242529 A242530 * A242532 A242533 A242534

KEYWORD

nonn,hard,more

AUTHOR

Stanislav Sykora, May 30 2014

EXTENSIONS

a(24)-a(28) from Fausto A. C. Cariboni, May 25 2017

STATUS

approved

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Last modified August 20 09:36 EDT 2017. Contains 290835 sequences.