A209487 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
11, 136, 731, 2606, 7179, 16660, 34233, 64220, 112263, 185506, 292759, 444680, 653957, 935472, 1306483, 1786806, 2398979, 3168444, 4123729, 5296612, 6722303, 8439626, 10491183, 12923536, 15787389, 19137752, 23034123, 27540670, 32726395
Offset: 1
Keywords
Examples
Some solutions for n=8: -6 -8 -6 -7 -8 -7 -7 -8 -8 -4 -5 -6 -8 -8 -6 -8 -1 -3 -6 -6 -2 0 -5 0 -4 -3 3 -2 1 -2 -3 3 2 -1 0 6 6 6 2 -2 -5 6 -2 3 -4 7 -4 -4 -2 -1 -3 2 -1 -7 5 -3 8 -3 -4 6 -3 -4 4 6 6 6 7 4 6 6 6 5 8 -4 2 -3 8 4 1 -1 1 7 8 1 -1 2 -1 8 1 8 6 2 6 3 8 4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8) for n > 9.
Comments