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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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

Andrew Howroyd, Table of n, a(n) for n = 1..100

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

FORMULA

Empirical: a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5) for n>7. - Andrew Howroyd, Apr 08 2016

Empirical G.f.: x^2 + ((1-x)^2*(1+x)^2)/(1-x-x^2-x^4-x^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

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.