A209345 Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal

4, 15, 35, 72, 128, 205, 311, 448, 618, 829, 1083, 1382, 1734, 2141, 2605, 3134, 3730, 4395, 5137, 5958, 6860, 7851, 8933, 10108, 11384, 12763, 14247, 15844, 17556, 19385, 21339, 23420, 25630, 27977, 30463, 33090, 35866, 38793, 41873, 45114, 48518, 52087

Offset

1,1

Comments

Row 4 of A209344.

Links

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

Formula

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

Empirical g.f.: x*(4 + 3*x + 2*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x + x^2)). - Colin Barker, Mar 07 2018

Example

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

Crossrefs

Cf. A209344.

Sequence in context: A113693 A211537 A213420 * A323452 A330204 A190093

Adjacent sequences: A209342 A209343 A209344 * A209346 A209347 A209348

Keyword

nonn

Author

R. H. Hardin, Mar 06 2012

Status

approved