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A208971
Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.
1
1, 3, 4, 8, 11, 18, 24, 35, 45, 61, 76, 98, 119, 148, 176, 213, 249, 295, 340, 396, 451, 518, 584, 663, 741, 833, 924, 1030, 1135, 1256, 1376, 1513, 1649, 1803, 1956, 2128, 2299, 2490, 2680, 2891, 3101, 3333, 3564, 3818, 4071, 4348, 4624, 4925, 5225, 5551, 5876
OFFSET
1,2
COMMENTS
Row 4 of A208970.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Conjectures from Colin Barker, Jul 07 2018: (Start)
G.f.: x*(1 + x - 3*x^2 + x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
a(n) = (2*n^3 + 6*n^2 + 28*n + 48) / 48 for n even.
a(n) = (2*n^3 + 6*n^2 + 22*n + 18) / 48 for n odd.
(End)
EXAMPLE
All solutions for n=5:
-2 -1 -2 -2 -1 -1 -1 0 -2 -2 -1
0 -1 0 -1 0 0 1 0 -1 -2 -1
2 0 1 1 0 1 -1 0 2 2 1
0 2 1 2 1 0 1 0 1 2 1
CROSSREFS
Cf. A208970.
Sequence in context: A156056 A236453 A099108 * A001994 A212544 A349801
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 03 2012
STATUS
approved