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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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2012
STATUS
approved

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Last modified February 26 04:47 EST 2024. Contains 370335 sequences. (Running on oeis4.)