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A078628
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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).
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9
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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; internal format)
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OFFSET
| 1,4
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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 E. Lambert (lamberti09(AT)mail.wlu.edu), Oct 07 2009]
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LINKS
| 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.
Isaac Lambert, Table of n, a(n) for n = 1..50
N. J. A. Sloane, FORTRAN program
Index entries for sequences related to shoe lacings
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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.
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CROSSREFS
| Cf. A078673. See A002816, A078603 for analogous sequence with restrictions only on pairs.
Cf. A095816, A165963, A165964. [From Isaac E. Lambert (lamberti09(AT)mail.wlu.edu), Oct 07 2009]
Sequence in context: A052558 A190340 A133666 * A165261 A027145 A010370
Adjacent sequences: A078625 A078626 A078627 * A078629 A078630 A078631
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 12 2002
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EXTENSIONS
| a(11)-a(13) from John W. Layman (layman(AT)math.vt.edu), Nov 15 2004
a(14) from Isaac E. Lambert (lamberti09(AT)mail.wlu.edu), Oct 07 2009
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