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A209074
Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2.
1
8, 70, 276, 766, 1722, 3378, 6006, 9928, 15514, 23180, 33380, 46624, 63464, 84498, 110368, 141766, 179426, 224134, 276714, 338040, 409034, 490664, 583936, 689912, 809696, 944438, 1095332, 1263622, 1450594, 1657586, 1885974, 2137184, 2412690
OFFSET
1,1
COMMENTS
Row 5 of A209073.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-6) - 2*a(n-7) + 3*a(n-8) - 3*a(n-9) + a(n-10).
Empirical g.f.: 2*x*(4 + 23*x + 45*x^2 + 66*x^3 + 64*x^4 + 49*x^5 + 21*x^6 + 4*x^7) / ((1 - x)^5*(1 + x)*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 08 2018
EXAMPLE
Some solutions for n=6:
-6 -3 -6 -3 -4 -4 -6 -2 -3 -3 -5 -4 -6 -3 -4 -3
3 0 5 -1 5 -1 6 -2 1 5 -4 5 3 -1 1 1
3 -1 0 -3 -1 6 2 0 2 -2 6 4 6 2 6 0
4 0 -3 3 0 0 -3 2 1 0 6 -3 -2 4 -2 -1
-4 4 4 4 0 -1 1 2 -1 0 -3 -2 -1 -2 -1 3
CROSSREFS
Cf. A209073.
Sequence in context: A335114 A226597 A376855 * A124152 A293069 A056631
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 04 2012
STATUS
approved