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A209009
Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
1
1, 5, 13, 31, 71, 137, 243, 399, 619, 927, 1329, 1857, 2525, 3355, 4385, 5627, 7121, 8893, 10971, 13407, 16213, 19449, 23143, 27333, 32083, 37413, 43389, 50053, 57447, 65651, 74683, 84631, 95537, 107455, 120475, 134625, 149997, 166649, 184637
OFFSET
1,2
COMMENTS
Row 5 of A209007.
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19).
EXAMPLE
Some solutions for n=6:
-2 -1 -3 -2 -2 -3 -2 -1 -3 -2 -3 -3 -1 -4 -4 -2
-1 -1 -2 1 1 -2 -1 -1 -1 0 -3 0 0 -3 1 0
0 2 0 0 -1 2 2 0 3 2 1 0 1 3 4 2
3 0 3 2 1 1 1 1 3 1 3 3 0 4 2 0
0 0 2 -1 1 2 0 1 -2 -1 2 0 0 0 -3 0
CROSSREFS
Sequence in context: A335307 A067333 A369176 * A118646 A097969 A082280
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 04 2012
STATUS
approved