A209488 Number of 7-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.

15, 458, 3740, 17771, 60778, 168453, 401634, 857433, 1679810, 3074315, 5321674, 8796771, 13984178, 21501971, 32119660, 46785813, 66648788, 93089119, 127741326, 172532039, 229703658, 301856427, 391974770, 503474661, 640230118, 806627193

Offset: 1

Author

R. H. Hardin, Mar 09 2012

Keywords

• nonn

Comments

Row 7 of A209485.

Examples

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

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-9) - a(n-13) - 2*a(n-14) + 2*a(n-15) - a(n-16) + a(n-17) + a(n-19) - 2*a(n-21) + a(n-22) for n > 24.