

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, i1, i2 (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
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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, i1, i2, 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: A190340 A232325 A133666 * A244058 A165261 A027145
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



