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A351356
Triangle read by rows T(n,k): number of binary necklaces with n beads, k of them black, and at least two consecutive black beads.
6
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 3, 3, 1, 1, 0, 0, 1, 4, 5, 3, 1, 1, 0, 0, 1, 5, 9, 7, 4, 1, 1, 0, 0, 1, 6, 13, 14, 10, 4, 1, 1, 0, 0, 1, 7, 19, 25, 22, 12, 5, 1, 1, 0, 0, 1, 8, 25, 41, 42, 30, 15, 5, 1, 1, 0, 0, 1, 9, 33, 63, 79, 66, 43, 19, 6, 1, 1, 0, 0, 1, 10, 41, 92, 131, 132, 99, 55, 22, 6, 1, 1
OFFSET
1,18
LINKS
Marko R. Riedel et al., Necklaces made of black and white beads, Math StackExchange, Feb 2022.
EXAMPLE
Triangle begins:
0;
0, 0;
0, 1, 0;
0, 1, 1, 0;
0, 1, 1, 1, 0;
0, 1, 2, 1, 1, 0;
0, 1, 3, 3, 1, 1, 0;
0, 1, 4, 5, 3, 1, 1, 0;
0, 1, 5, 9, 7, 4, 1, 1, 0;
...
CROSSREFS
Row sums are A351359.
Sequence in context: A208249 A329985 A029422 * A152800 A223730 A353129
KEYWORD
nonn,tabl
AUTHOR
Marko Riedel, Feb 08 2022
STATUS
approved