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

1,1

Comments

Row 7 of A209344.

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).

Example

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

Crossrefs

Sequence in context: A065921 A129993 A359852 * A095655 A221766 A080483

Adjacent sequences: A209345 A209346 A209347 * A209349 A209350 A209351

Keyword

nonn

Author

R. H. Hardin, Mar 06 2012

Status

approved