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A209347 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal. 1
14, 146, 770, 2698, 7358, 16968, 34720, 64942, 113288, 186906, 294616, 447084, 657006, 939270, 1311146, 1792454, 2405742, 3176460, 4133144, 5307578, 6734984, 8454190, 10507808, 12942408, 15808702, 19161706, 23060930, 27570546, 32759566 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 6 of A209344.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) - 5*a(n-7) + 4*a(n-8) - a(n-9).

Empirical g.f.: 2*x*(7 + 45*x + 128*x^2 + 167*x^3 + 128*x^4 + 48*x^5 + 5*x^6) / ((1 - x)^6*(1 + x)*(1 + x + x^2)). - Colin Barker, Jul 09 2018

EXAMPLE

Some solutions for n=8:

  -5  -8  -6  -2  -4  -6  -6  -3  -3  -8  -8  -6  -5  -4  -5  -8

  -4   1  -1  -2  -1  -5  -3  -1  -1   0  -3  -1   1  -2   2  -7

  -2  -2   4   0   5  -2   5   1   2  -4   7   1  -2   1   4   8

   4   3  -4   0  -4   2   5   2  -3  -2   3   3  -3   2   0   6

   7   1  -1   1   4   3  -5  -3   1   7  -7  -3   7   3  -4   3

   0   5   8   3   0   8   4   4   4   7   8   6   2   0   3  -2

CROSSREFS

Cf. A209344.

Sequence in context: A099914 A016278 A241169 * A132934 A027473 A002451

Adjacent sequences:  A209344 A209345 A209346 * A209348 A209349 A209350

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 06 2012

STATUS

approved

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Last modified October 22 11:41 EDT 2021. Contains 348168 sequences. (Running on oeis4.)