

A242525


Number of cyclic arrangements of S={1,2,...,n} such that the difference between any two neighbors is at most 3.


16



1, 1, 1, 3, 6, 10, 17, 31, 57, 104, 188, 340, 616, 1117, 2025, 3670, 6651, 12054, 21847, 39596, 71764, 130065, 235730, 427238, 774328, 1403395, 2543518, 4609881, 8354965, 15142569, 27444447, 49740415, 90149708, 163387657, 296124381, 536696900
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OFFSET

1,4


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.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..100
S. Sykora, On NeighborProperty Cycles, Stan's Library, Volume V, 2014.


FORMULA

Empirical: a(n) = a(n1)+a(n2)+a(n4)+a(n5) for n>7.  Andrew Howroyd, Apr 08 2016
Empirical G.f.: x^2 + ((1x)^2*(1+x)^2)/(1xx^2x^4x^5).  Andrew Howroyd, Apr 08 2016


EXAMPLE

For n=4, The three cycles are: C_1={1,2,3,4}, C_2={1,2,4,3}, C_3={1,3,2,4}.
The first and the last of the 104 such cycles of length n=10 are: C_1={1,2,3,5,6,8,9,10,7,4}, C_104={1,3,6,9,10,8,7,5,2,4}.


PROG

(C++) See the link.


CROSSREFS

Cf. A242519, A242520, A242521, A242522, A242523, A242524, A242526, A242527, A242528, A242529, A242530, A242531, A242532, A242533, A242534.
Sequence in context: A069241 A092263 A259968 * A266617 A182152 A170803
Adjacent sequences: A242522 A242523 A242524 * A242526 A242527 A242528


KEYWORD

nonn


AUTHOR

Stanislav Sykora, May 27 2014


EXTENSIONS

a(28)a(35) from Andrew Howroyd, Apr 08 2016


STATUS

approved



