[seqfan] easy? graph question

[Neil Sloane]

Dear Seq Fans,  Someone just asked me to explain A085680, which is:


Size of largest code of length n and constant weight 2 that can
correct a single adjacent transposition.  The data line gives only
these values, with offset 2:

1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 15, 17, 20, 23, 26, 29, 32, 36, 40,
44, 48, 52, 57, 62

I just added an explanation, as follows:

Look at the set of n-choose-2 binary vectors of length n with exactly
two 1's and n-2 0's in each vector.

If we can get a vector v from a vector u by swapping 2 adjacent
coordinates, say that u and v are adjacent.

a(n) is the maximal number of nodes in the resulting graph that are
separated by at least three edges.

For n=4 the graph is

.................1001

................../....\

1100--1010......0101--0011

..................\..../

..................0110

so a(4) = 2 (use 1100 and 0011 as the code, or 1100 and 0101).

More terms, anyone?