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

1,33

Links

Table of n, a(n) for n=1..104.

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

Formula

Row sums are A351361.

Example

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;

Crossrefs

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

Sequence in context: A321923 A064663 A025923 * A138158 A057276 A259829

Adjacent sequences: A351355 A351356 A351357 * A351359 A351360 A351361

Keyword

nonn,tabf

Author

Marko Riedel, Feb 08 2022

Status

approved