A209486 Number of 5-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.

4, 38, 140, 390, 866, 1702, 3014, 4984, 7774, 11620, 16716, 23352, 31768, 42302, 55232, 70950, 89774, 112150, 138434, 169120, 204610, 245452, 292080, 345096, 404980, 472382, 547820, 631998, 725474, 829006, 943190, 1068832, 1206574

Offset

1,1

Comments

Row 5 of A209485.

Links

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

Formula

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

Empirical g.f.: 2*x*(2 + 15*x + 32*x^2 + 57*x^3 + 62*x^4 + 59*x^5 + 34*x^6 + 13*x^7 + 2*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 10 2018

Example

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

Crossrefs

Cf. A209485.

Sequence in context: A003633 A129310 A152110 * A245129 A196851 A196702

Adjacent sequences: A209483 A209484 A209485 * A209487 A209488 A209489

Keyword

nonn

Author

R. H. Hardin, Mar 09 2012

Status

approved