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A208828 Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero. 1
32, 609, 4390, 19657, 65134, 177097, 417204, 883409, 1720628, 3135633, 5410378, 8921049, 14153874, 21728505, 32416136, 47167393, 67132584, 93694273, 128489486, 173447145, 230812054, 303187369, 393560188, 505349233, 642431868, 809197169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A208825.

LINKS

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

FORMULA

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 8*a(n-3) + 14*a(n-4) - 14*a(n-6) + 8*a(n-7) + 3*a(n-8) - 4*a(n-9) + a(n-10).

Empirical g.f.: x*(32 + 481*x + 2050*x^2 + 4180*x^3 + 4100*x^4 + 2126*x^5 + 462*x^6 + 28*x^7 - 4*x^8 + x^9) / ((1 - x)^7*(1 + x)^3). - Colin Barker, Jul 07 2018

EXAMPLE

Some solutions for n=3:

  -3  -3  -2  -3  -3  -3  -3  -3  -3  -3  -3  -2  -3  -1  -3  -2

   1  -1  -2  -1   2  -2   1  -1  -2  -2   3  -2   2  -1  -1  -1

  -1   3   0  -2   0   2  -1   1   1  -1   0  -1  -2   0  -1   1

  -1   1   1  -1   1   1   2   1   3   2  -2  -1   0   0   1  -1

   1   0   2   2  -2   2  -3   1  -3   2  -2   3   1   1   1  -1

   2  -2  -1   3  -1  -2   1   2   3   3   1   0   0   1   2   3

   1   2   2   2   3   2   3  -1   1  -1   3   3   2   0   1   1

CROSSREFS

Cf. A208825.

Sequence in context: A332262 A088914 A036903 * A013699 A283279 A004337

Adjacent sequences:  A208825 A208826 A208827 * A208829 A208830 A208831

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2012

STATUS

approved

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Last modified May 31 00:16 EDT 2020. Contains 334747 sequences. (Running on oeis4.)