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

1,1

Comments

Row 5 of A209344.

Links

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

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

Example

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

Crossrefs

Cf. A209344.

Sequence in context: A015874 A244725 A319098 * A027264 A025214 A222613

Adjacent sequences: A209343 A209344 A209345 * A209347 A209348 A209349

Keyword

nonn

Author

R. H. Hardin, Mar 06 2012

Status

approved