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A209346
Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.
1
5, 40, 145, 400, 883, 1724, 3045, 5026, 7827, 11684, 16795, 23446, 31879, 42430, 55379, 71118, 89965, 112362, 138671, 169384, 204901, 245770, 292429, 345476, 405393, 472828, 548301, 632516, 726031, 829600, 943825, 1069510, 1207295
OFFSET
1,1
COMMENTS
Row 5 of A209344.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-4) + a(n-5) + 3*a(n-6) - a(n-7) - 2*a(n-8) + a(n-9).
Empirical g.f.: x*(5 + 30*x + 60*x^2 + 85*x^3 + 63*x^4 + 28*x^5 + 4*x^6 + x^7) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jul 09 2018
EXAMPLE
Some solutions for n=10:
-9 -7 -10 -5 -10 -10 -8 -7 -8 -7 -9 -7 -4 -6 -10 -8
5 4 -4 -1 -4 -5 -7 -3 1 0 -4 2 -2 1 -4 -3
7 -3 -5 3 4 -1 8 -3 6 -1 9 -3 -2 4 10 8
-9 -1 10 3 5 10 3 3 -1 3 3 2 10 -2 6 1
6 7 9 0 5 6 4 10 2 5 1 6 -2 3 -2 2
CROSSREFS
Cf. A209344.
Sequence in context: A015874 A244725 A319098 * A027264 A025214 A222613
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2012
STATUS
approved