A209346 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal.

5, 40, 145, 400, 883, 1724, 3045, 5026, 7827, 11684, 16795, 23446, 31879, 42430, 55379, 71118, 89965, 112362, 138671, 169384, 204901, 245770, 292429, 345476, 405393, 472828, 548301, 632516, 726031, 829600, 943825, 1069510, 1207295

Offset: 1

Author

R. H. Hardin, Mar 06 2012

Keywords

• nonn

Comments

Row 5 of A209344.

Examples

			Some solutions for n=10:
  -9  -7 -10  -5 -10 -10  -8  -7  -8  -7  -9  -7  -4  -6 -10  -8
   5   4  -4  -1  -4  -5  -7  -3   1   0  -4   2  -2   1  -4  -3
   7  -3  -5   3   4  -1   8  -3   6  -1   9  -3  -2   4  10   8
  -9  -1  10   3   5  10   3   3  -1   3   3   2  10  -2   6   1
   6   7   9   0   5   6   4  10   2   5   1   6  -2   3  -2   2
		

Links

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

Crossrefs

Cf. A209344.

Formula

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

Empirical g.f.: x*(5 + 30*x + 60*x^2 + 85*x^3 + 63*x^4 + 28*x^5 + 4*x^6 + x^7) / ((1 - x)^5*(1 + x)^2*(1 + x + x^2)). - Colin Barker, Jul 09 2018