A208996 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.

3, 17, 59, 159, 351, 683, 1207, 1989, 3099, 4623, 6647, 9277, 12615, 16787, 21913, 28137, 35597, 44455, 54867, 67015, 81071, 97237, 115701, 136685, 160395, 187071, 216937, 250251, 287255, 328227, 373425, 423147, 477667, 537303, 602347, 673135

Offset

1,1

Comments

Row 5 of A208993.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 3*a(n-5) - 3*a(n-6) - a(n-7) + 4*a(n-8) - a(n-9) - 2*a(n-10) + a(n-11).

Empirical g.f.: x*(3 + 11*x + 22*x^2 + 36*x^3 + 39*x^4 + 32*x^5 + 25*x^6 + 14*x^7 - x^9 + x^10) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jul 07 2018

Example

Some solutions for n=6:
  -5 -3 -5 -5 -3 -5 -1 -3 -3 -3 -3 -5 -2 -4 -1 -4
  -1 -1 -2  1  1  1  0  2 -2  1 -3  0 -1 -1  0 -4
   2  2  4  4  2  1 -1  0  0 -3 -1  4 -2  0 -1  0
   4  1  3  0  0  4  2 -1  3  2  4  3  3  4  0  6
   0  1  0  0  0 -1  0  2  2  3  3 -2  2  1  2  2

Crossrefs

Cf. A208993.

Sequence in context: A130857 A226719 A168547 * A273949 A174285 A227427

Adjacent sequences: A208993 A208994 A208995 * A208997 A208998 A208999

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved