

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, 347675502245
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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..32.
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


AUTHOR

Stanislav Sykora, May 27 2014


EXTENSIONS

a(27)a(30) from Max Alekseyev, Jul 12 2014
a(31)a(32) from Fausto A. C. Cariboni, May 17 2017, May 24 2017


STATUS

approved



