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A209073 T(n,k) = number of n-bead necklaces labeled with numbers -k..k not allowing reversal, with sum zero and avoiding the pattern z z+1 z+2. 12
1, 1, 2, 1, 3, 2, 1, 4, 6, 5, 1, 5, 12, 22, 8, 1, 6, 20, 57, 70, 19, 1, 7, 30, 122, 276, 265, 39, 1, 8, 42, 223, 766, 1465, 1007, 95, 1, 9, 56, 366, 1722, 5239, 8008, 4055, 223, 1, 10, 72, 563, 3378, 14431, 37108, 45408, 16593, 554, 1, 11, 90, 820, 6006, 33469, 125428 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Table starts

   1    1     1      1       1       1        1        1        1         1

   2    3     4      5       6       7        8        9       10        11

   2    6    12     20      30      42       56       72       90       110

   5   22    57    122     223     366      563      820     1143      1544

   8   70   276    766    1722    3378     6006     9928    15514     23180

  19  265  1465   5239   14431   33469    68723   128845   225127    371859

  39 1007  8008  37108  125428  344618   817594  1738838  3397900   6206228

  95 4055 45408 271732 1125484 3660116 10030238 24194286 52868486 106770774

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..166

EXAMPLE

Some solutions for n=6, k=6:

  -6  -5  -5  -4  -6  -6  -4  -5  -6  -5  -5  -6  -6  -4  -4  -6

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

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

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

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

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

CROSSREFS

Row 3 is A002378.

Row 4 is A208946.

Sequence in context: A066121 A039911 A208945 * A332077 A220901 A002335

Adjacent sequences:  A209070 A209071 A209072 * A209074 A209075 A209076

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 04 2012

STATUS

approved

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Last modified May 16 11:14 EDT 2022. Contains 353704 sequences. (Running on oeis4.)