A078628 - OEIS

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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).

1, 1, 0, 4, 12, 76, 494, 3662, 30574, 284398, 2918924, 32791604, 400400062, 5281683678, 74866857910, 1135063409918, 18330526475060, 314169905117860, 5695984717957246, 108921059813769710, 2190998123920252622, 46250325111346491694

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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 * A358660 A301340 A244058