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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

%I #24 Aug 11 2014 22:45:23

%S 1,1,0,4,12,76,494,3662,30574,284398,2918924,32791604,400400062,

%T 5281683678,74866857910,1135063409918,18330526475060,314169905117860,

%U 5695984717957246,108921059813769710,2190998123920252622,46250325111346491694

%N 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).

%C 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]

%D 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

%H Isaac Lambert, <a href="/A078628/b078628.txt">Table of n, a(n) for n = 1..50</a>

%H W. Dymacek and I. Lambert, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Dymacek/dymacek5.html">Circular Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2</a>, Journal of Integer Sequences, Vol. 14 (2011), Article 11.1.6.

%H N. J. A. Sloane, <a href="/A078628/a078628.txt">FORTRAN program</a>

%H <a href="/index/La#lacings">Index entries for sequences related to shoe lacings</a>

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

%e 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.

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

%Y Cf. A095816, A165963, A165964. [From _Isaac Lambert_, Oct 07 2009]

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Dec 12 2002

%E a(11)-a(13) from _John W. Layman_, Nov 15 2004

%E a(14) from _Isaac Lambert_, Oct 07 2009