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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
OFFSET
1,1
COMMENTS
Row 7 of A208825.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2012
STATUS
approved