A209033 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first differences in -n..n.

2, 11, 34, 88, 187, 358, 625, 1023, 1584, 2355, 3374, 4700, 6377, 8476, 11049, 14175, 17916, 22361, 27580, 33672, 40713, 48816, 58063, 68577, 80448, 93809, 108760, 125442, 143963, 164476, 187095, 211985, 239266, 269115, 301660, 337086, 375531

Offset: 1

Author

R. H. Hardin, Mar 04 2012

Keywords

• nonn

Comments

Row 5 of A209032.

Examples

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

Links

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

Crossrefs

Cf. A209032.

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) - 2*a(n-6) + 2*a(n-7) + a(n-8) - 2*a(n-9) + 2*a(n-10) - 2*a(n-12) + a(n-13).

Empirical g.f.: x*(2 + 7*x + 12*x^2 + 24*x^3 + 29*x^4 + 32*x^5 + 32*x^6 + 23*x^7 + 12*x^8 + 9*x^9 - x^11 + x^12) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Jul 07 2018