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A209346 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 03:38 EDT 2021. Contains 348141 sequences. (Running on oeis4.)