A351358 Irregular triangle read by rows T(n,k): number of binary necklaces with n beads, k of them black, and at least four consecutive black beads.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 0, 1, 3, 3, 1, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 1, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 1, 0, 0, 0, 0, 1, 6, 15, 20, 14, 5, 1, 1, 0, 0, 0, 0, 1, 7, 21, 35, 34, 18, 6, 1, 1, 0, 0, 0, 0, 1, 8, 28, 56, 68, 50, 22, 6, 1, 1

Offset: 1

Author

Marko Riedel, Feb 08 2022

Keywords

• nonn
• tabf

Examples

			Triangle begins:
  0, 0;
  0, 0, 0;
  0, 0, 0, 0;
  0, 0, 0, 0, 1;
  0, 0, 0, 0, 1, 1;
  0, 0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 1, 2, 1, 1;
  0, 0, 0, 0, 1, 3, 3, 1, 1;
		

Links

• Marko R. Riedel et al., Necklaces made of black and white beads, Math StackExchange, Feb 2022.

Crossrefs

Cf. A351356, A351357, A351359, A351360, A351361.

Formula

Row sums are A351361.