A208995 Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.

2, 7, 16, 33, 58, 95, 144, 209, 290, 391, 512, 657, 826, 1023, 1248, 1505, 1794, 2119, 2480, 2881, 3322, 3807, 4336, 4913, 5538, 6215, 6944, 7729, 8570, 9471, 10432, 11457, 12546, 13703, 14928, 16225, 17594, 19039, 20560, 22161, 23842, 25607, 27456, 29393

Offset

1,1

Comments

Row 4 of A208993.

Links

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

Formula

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

Conjectures from Colin Barker, Jul 07 2018: (Start)

G.f.: x*(2 + x - x^2 + 3*x^3 - x^4) / ((1 - x)^4*(1 + x)).

a(n) = (12 + 8*n + 6*n^2 + 4*n^3) / 12 for n even.

a(n) = (6 + 8*n + 6*n^2 + 4*n^3) / 12 for n odd.

(End)

Example

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

Crossrefs

Cf. A208993.

Sequence in context: A333395 A130869 A212576 * A023612 A192952 A132738

Adjacent sequences: A208992 A208993 A208994 * A208996 A208997 A208998

Keyword

nonn

Author

R. H. Hardin, Mar 04 2012

Status

approved