A351357 - OEIS

A351357

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

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 3, 3, 1, 1, 0, 0, 0, 1, 4, 6, 4, 1, 1, 0, 0, 0, 1, 5, 10, 9, 4, 1, 1, 0, 0, 0, 1, 6, 15, 19, 12, 5, 1, 1, 0, 0, 0, 1, 7, 21, 33, 29, 15, 5, 1, 1, 0, 0, 0, 1, 8, 28, 54, 60, 42, 19, 6, 1, 1, 0, 0, 0, 1, 9, 36, 81, 111, 96, 55, 22, 6, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,25

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.

EXAMPLE

Triangle begins:

0, 0;

0, 0, 0;

0, 0, 0, 1;

0, 0, 0, 1, 1;

0, 0, 0, 1, 1, 1;

0, 0, 0, 1, 2, 1, 1;

0, 0, 0, 1, 3, 3, 1, 1;

0, 0, 0, 1, 4, 6, 4, 1, 1;

CROSSREFS

Row sums are A351360.

Cf. A351356, A351358, A351359, A351361.

Sequence in context: A225230 A367106 A328084 * A263250 A209287 A025901

Adjacent sequences: A351354 A351355 A351356 * A351358 A351359 A351360

KEYWORD

nonn,tabf

AUTHOR

Marko Riedel, Feb 08 2022

STATUS

approved