|
|
A208599
|
|
Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
|
|
2
|
|
|
11, 77, 291, 791, 1761, 3431, 6077, 10021, 15631, 23321, 33551, 46827, 63701, 84771, 110681, 142121, 179827, 224581, 277211, 338591, 409641, 491327, 584661, 690701, 810551, 945361, 1096327, 1264691, 1451741, 1658811, 1887281, 2138577, 2414171
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = (23/12)*n^4 + (23/6)*n^3 + (37/12)*n^2 + (7/6)*n + 1.
G.f.: x*(11 + 22*x + 16*x^2 - 4*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
|
|
EXAMPLE
|
Some solutions for n=4:
-4 -3 -4 -4 -3 -3 -3 -3 -3 -4 -4 -4 -4 -4 -4 -1
-1 2 3 2 0 2 1 -1 4 2 0 -1 4 0 0 0
4 -2 2 -4 -3 2 2 2 0 0 0 4 -3 2 -1 1
-2 3 0 3 3 -1 -2 0 1 -2 2 1 4 1 2 -1
3 0 -1 3 3 0 2 2 -2 4 2 0 -1 1 3 1
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|