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A209487 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2. 1
11, 136, 731, 2606, 7179, 16660, 34233, 64220, 112263, 185506, 292759, 444680, 653957, 935472, 1306483, 1786806, 2398979, 3168444, 4123729, 5296612, 6722303, 8439626, 10491183, 12923536, 15787389, 19137752, 23034123, 27540670, 32726395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 6 of A209485.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (5, -10, 11, -10, 11, -10, 5, -1).

FORMULA

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8) for n > 9.

EXAMPLE

Some solutions for n=8:

  -6  -8  -6  -7  -8  -7  -7  -8  -8  -4  -5  -6  -8  -8  -6  -8

  -1  -3  -6  -6  -2   0  -5   0  -4  -3   3  -2   1  -2  -3   3

   2  -1   0   6   6   6   2  -2  -5   6  -2   3  -4   7  -4  -4

  -2  -1  -3   2  -1  -7   5  -3   8  -3  -4   6  -3  -4   4   6

   6   6   7   4   6   6   6   5   8  -4   2  -3   8   4   1  -1

   1   7   8   1  -1   2  -1   8   1   8   6   2   6   3   8   4

MATHEMATICA

Join[{11}, LinearRecurrence[{5, -10, 11, -10, 11, -10, 5, -1}, {136, 731, 2606, 7179, 16660, 34233, 64220, 112263}, 40]] (* Harvey P. Dale, Feb 04 2013 *)

CROSSREFS

Sequence in context: A250460 A157773 A336180 * A227101 A024143 A057718

Adjacent sequences:  A209484 A209485 A209486 * A209488 A209489 A209490

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 09 2012

STATUS

approved

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Last modified September 19 13:25 EDT 2020. Contains 337178 sequences. (Running on oeis4.)