A376921 Number T(n,k) of binary words of length n avoiding distance (i+1) between "1" digits if the i-th bit is set in the binary representation of k; triangle T(n,k), n>=0, 0<=k<=ceiling(2^(n-1))-1, read by rows.

1, 2, 4, 3, 8, 5, 6, 4, 16, 8, 9, 6, 12, 7, 8, 5, 32, 13, 15, 9, 18, 11, 11, 7, 24, 11, 12, 8, 16, 9, 10, 6, 64, 21, 25, 13, 27, 16, 17, 10, 36, 17, 16, 11, 21, 12, 13, 8, 48, 18, 21, 12, 24, 15, 14, 9, 32, 14, 15, 10, 20, 11, 12, 7

Offset: 0

Author

Alois P. Heinz, Oct 10 2024

Keywords

• nonn
• tabf

Comments

For more information see A376033.

Examples

			Triangle T(n,k) begins:
   1;
   2;
   4,  3;
   8,  5,  6, 4;
  16,  8,  9, 6, 12,  7,  8, 5;
  32, 13, 15, 9, 18, 11, 11, 7, 24, 11, 12, 8, 16, 9, 10, 6;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..16, flattened

Crossrefs

Cf. A376033.

Programs

Maple

h:= proc(n) option remember; `if`(n=0, 1, 2^(1+ilog2(n))) end:
b:= proc(n, k, t) option remember; `if`(n=0, 1, add(`if`(j=1 and
      Bits[And](t, k)>0, 0, b(n-1, k, irem(2*t+j, h(k)))), j=0..1))
    end:
T:= (n, k)-> b(n, k, 0):
seq(seq(T(n, k), k=0..ceil(2^(n-1))-1), n=0..7);