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A208600 Number of 6-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero. 2
26, 297, 1564, 5457, 14838, 34153, 69784, 130401, 227314, 374825, 590580, 895921, 1316238, 1881321, 2625712, 3589057, 4816458, 6358825, 8273228, 10623249, 13479334, 16919145, 21027912, 25898785, 31633186, 38341161, 46141732, 55163249 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 6 of A208597.
LINKS
FORMULA
Empirical: a(n) = (44/15)*n^5 + (22/3)*n^4 + (23/3)*n^3 + (14/3)*n^2 + (12/5)*n + 1.
Conjectures from Colin Barker, Mar 07 2018: (Start)
G.f.: x*(26 + 141*x + 172*x^2 + 8*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
EXAMPLE
Some solutions for n=4:
-4 -4 -4 -3 -4 -2 -4 -4 -4 -4 -3 -4 -4 -3 -3 -1
4 3 2 2 -3 -2 -1 2 0 -1 3 4 2 -1 3 0
0 2 -1 3 -2 2 0 -3 4 2 -3 -2 1 2 0 -1
1 1 -3 0 3 0 -1 0 -1 1 3 0 3 -2 -2 0
-1 1 3 0 4 -2 4 3 4 4 -3 1 -2 4 0 -1
0 -3 3 -2 2 4 2 2 -3 -2 3 1 0 0 2 3
CROSSREFS
Sequence in context: A020925 A224331 A125414 * A010831 A022718 A014472
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 29 2012
STATUS
approved

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Last modified April 22 21:44 EDT 2024. Contains 371906 sequences. (Running on oeis4.)