
COMMENTS

See A210109 for further information.
It appears that A027376 gives the number of 2divided words that have a unique division into two parts.  David Scambler, Mar 21 2012
Row sums of the following irregular triangle W(n,k) which shows how many words of length n over a 3letter alphabet are 2divided in k>=1 different ways (3letter analog of A209919):
3;
8, 8;
18, 21, 18;
48, 48, 48, 48;
116, 124, 119, 124, 116;
312, 312, 312, 312, 312, 312;
810, 828, 810, 831, 810, 828, 810;
2184, 2184, 2192, 2184, 2184, 2192, 2184, 2184;
5880, 5928, 5880, 5928, 5883, 5928, 5880, 5928, 5880;
First column of the following triangle D(n,k) which shows how many words of length n over a 3letter alphabet are kdivided:
3;
16, 1;
57, 16, 0;
192, 78, 6, 0;
599, 324, 56, 0, 0;
1872, 1141, 343, 15, 0, 0;
5727, 3885, 1534, 166, 0, 0, 0;
17488, 12630, 6067, 1135, 20, 0, 0, 0;
53115, 40315, 22162, 5865, 351, 0, 0, 0, 0;
161040, 126604, ...
 R. J. Mathar, Mar 25 2012
Speculation: W(2n+1,2)=W(2n+1,1) and W(2n,2) = W(2n,1)+W(n,1). W(3n+1,3)=W(3n+1,1); W(3n+2,3)=W(3n+1,1); W(3n,3) = W(3n,1)+W(n,1).  R. J. Mathar, Mar 27 2012
