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.

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

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