A209348 Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

21, 514, 4029, 18646, 62853, 172610, 409199, 870122, 1699831, 3104474, 5365417, 8858142, 14068115, 21614144, 32266607, 46975088, 66888951, 93389664, 128113109, 172986976, 230254897, 302518564, 392763779, 504407780, 641326401, 807907094

Offset: 1

Author

R. H. Hardin, Mar 06 2012

Keywords

• nonn

Comments

Row 7 of A209344.

Examples

			Some solutions for n=5:
  -5  -4  -4  -5  -5  -4  -4  -3  -2  -2  -4  -4  -5  -5  -5  -4
  -5  -3   0  -4   0  -2  -3  -1  -1  -1  -3  -2  -2  -4  -3   1
  -1   5  -4   2   0  -2   1  -2  -1  -2   4   3  -1   0   5  -3
   5   5   1   2   5   0   1   2   1  -1   1   3   5   4   2  -2
  -4  -3   2   1  -1   2   5   2  -1   3   5  -4   3   2  -2   1
   5  -1   3  -1  -4   1   2   0   3   3  -4   0  -2   1   0   2
   5   1   2   5   5   5  -2   2   1   0   1   4   2   2   3   5
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - 2*a(n-5) + 5*a(n-6) - 5*a(n-7) + 3*a(n-8) - 3*a(n-10) + 5*a(n-11) - 5*a(n-12) + 2*a(n-13) - a(n-14) + a(n-15) + 2*a(n-16) - 3*a(n-17) + a(n-18).