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.

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

Author

Marko Riedel, Feb 08 2022

Keywords

• nonn
• tabl

Examples

			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;
  ...
		

Links

• Marko R. Riedel et al., Necklaces made of black and white beads, Math StackExchange, Feb 2022.
• Marko R. Riedel, Maple code for sequence from cited link.

Crossrefs

Row sums are A351359.

Cf. A351357, A351358, A351360, A351361.