

A242519


Number of cyclic arrangements of S={1,2,...,n} such that the difference between any two neighbors is 2^k for some k=0,1,2,...


17



0, 1, 1, 1, 4, 8, 14, 32, 142, 426, 1204, 3747, 9374, 26306, 77700, 219877, 1169656, 4736264, 17360564, 69631372, 242754286, 891384309, 3412857926, 12836957200, 42721475348, 152125749587, 549831594988
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OFFSET

1,5


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. Evaluating this sequence for n>=3 is equivalent to counting Hamiltonian cycles in a pairproperty graph with n vertices and is often quite hard. For more details, see the link.


LINKS

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..27 (first 21 terms from Stanislav Sykora)
S. Sykora, On NeighborProperty Cycles, Stan's Library, Volume V, 2014.


FORMULA

For any S and any P, and for n>=3, NPC(n;S;P)<=A001710(n1).


EXAMPLE

The four such cycles of length 5 are:
C_1={1,2,3,4,5}, C_2={1,2,4,3,5}, C_3={1,2,4,5,3}, C_4={1,3,2,4,5}.
The first and the last of the 426 such cycles of length 10 are:
C_1={1,2,3,4,5,6,7,8,10,9}, C_426={1,5,7,8,6,4,3,2,10,9}.


PROG

(C++) See the link.


CROSSREFS

Cf. A001710, A236602, A242520, A242521, A242522, A242523, A242524, A242525, A242526, A242527, A242528, A242529, A242530, A242531, A242532, A242533, A242534.
Sequence in context: A153364 A124743 A188575 * A174554 A272048 A112312
Adjacent sequences: A242516 A242517 A242518 * A242520 A242521 A242522


KEYWORD

nonn,hard


AUTHOR

Stanislav Sykora, May 27 2014


EXTENSIONS

a(22)a(27) from Hiroaki Yamanouchi, Aug 29 2014


STATUS

approved



