

A242521


Number of cyclic arrangements (up to direction) of {1,2,...,n} such that the difference between any two neighbors is b^k for some b>1 and k>1.


15



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 9, 42, 231, 1052, 3818, 10086, 27892, 90076, 310301, 993680, 4663558, 22038882, 162588454, 1246422151, 8655752023, 58951670318
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OFFSET

1,13


COMMENTS

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


LINKS

Table of n, a(n) for n=1..31.
S. Sykora, On NeighborProperty Cycles, Stan's Library, Volume V, 2014.


EXAMPLE

The two cycles of length n=13 (the smallest n such that a(n)>0) are: C_1={1,5,9,13,4,8,12,3,7,11,2,6,10}, C_2={1,9,5,13,4,8,12,3,7,11,2,6,10}.


PROG

(C++) See the link.


CROSSREFS

Cf. A242519, A242520, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242531, A242532, A242533, A242534.
Sequence in context: A271927 A227526 A093081 * A073659 A073661 A079052
Adjacent sequences: A242518 A242519 A242520 * A242522 A242523 A242524


KEYWORD

nonn,hard,more,changed


AUTHOR

Stanislav Sykora, May 27 2014


EXTENSIONS

a(27)a(30) from Max Alekseyev, Jul 12 2014
a(31) from Fausto A. C. Cariboni, May 17 2017


STATUS

approved



