A208599 Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.

11, 77, 291, 791, 1761, 3431, 6077, 10021, 15631, 23321, 33551, 46827, 63701, 84771, 110681, 142121, 179827, 224581, 277211, 338591, 409641, 491327, 584661, 690701, 810551, 945361, 1096327, 1264691, 1451741, 1658811, 1887281, 2138577, 2414171

Offset

1,1

Comments

Row 5 of A208597.

Links

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

Formula

Empirical: a(n) = (23/12)*n^4 + (23/6)*n^3 + (37/12)*n^2 + (7/6)*n + 1.

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

G.f.: x*(11 + 22*x + 16*x^2 - 4*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A208597.

Sequence in context: A272395 A305727 A218395 * A325733 A059625 A355053

Adjacent sequences: A208596 A208597 A208598 * A208600 A208601 A208602

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved