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A078628 Number of ways of arranging the numbers 1..n in a circle so that there is no consecutive triple i, i+1, i+2 or i, i-1, i-2 (mod n). 16
1, 1, 0, 4, 12, 76, 494, 3662, 30574, 284398, 2918924, 32791604, 400400062, 5281683678, 74866857910, 1135063409918, 18330526475060, 314169905117860, 5695984717957246, 108921059813769710, 2190998123920252622, 46250325111346491694 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This sequence can be related to A165964 by the use of auxiliary sequences (and the auxiliary sequences can themselves be calculated by recurrence relations). So if we desire we can determine any value of this sequence. [From Isaac Lambert, Oct 07 2009]

REFERENCES

Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012. - From N. J. A. Sloane, Sep 14 2012

LINKS

Isaac Lambert, Table of n, a(n) for n = 1..50

W. Dymacek and I. Lambert, Circular Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2, Journal of Integer Sequences, Vol. 14 (2011), Article 11.1.6.

N. J. A. Sloane, FORTRAN program

Index entries for sequences related to shoe lacings

EXAMPLE

a(4) = 4: 4 2 1 3, 4 3 1 2, 4 1 3 2, 4 2 3 1.

a(5) = 12: 5 3 1 2 4, 5 2 3 1 4, 5 4 2 1 3, 5 2 4 1 3, 5 1 4 2 3, 5 2 1 4 3, 5 1 3 4 2, 5 3 1 4 2, 5 4 1 3 2, 5 3 4 1 2, 5 2 4 3 1, 5 3 2 4 1.

CROSSREFS

Cf. A078673. See A002816, A078603 for analogous sequence with restrictions only on pairs.

Cf. A095816, A165963, A165964. [From Isaac Lambert, Oct 07 2009]

Sequence in context: A291487 A133666 A318432 * A301340 A244058 A165261

Adjacent sequences:  A078625 A078626 A078627 * A078629 A078630 A078631

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 12 2002

EXTENSIONS

a(11)-a(13) from John W. Layman, Nov 15 2004

a(14) from Isaac Lambert, Oct 07 2009

STATUS

approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)