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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

%I #14 Mar 13 2022 19:30:17

%S 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,

%T 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,

%U 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

%N 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.

%H Marko R. Riedel et al., <a href="https://math.stackexchange.com/questions/4376420/">Necklaces made of black and white beads</a>, Math StackExchange, Feb 2022.

%H Marko R. Riedel, <a href="/A351356/a351356.maple.txt">Maple code for sequence from cited link.</a>

%e Triangle begins:

%e 0;

%e 0, 0;

%e 0, 1, 0;

%e 0, 1, 1, 0;

%e 0, 1, 1, 1, 0;

%e 0, 1, 2, 1, 1, 0;

%e 0, 1, 3, 3, 1, 1, 0;

%e 0, 1, 4, 5, 3, 1, 1, 0;

%e 0, 1, 5, 9, 7, 4, 1, 1, 0;

%e ...

%Y Row sums are A351359.

%Y Cf. A351357, A351358, A351360, A351361.

%K nonn,tabl

%O 1,18

%A _Marko Riedel_, Feb 08 2022