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Triangle read by rows: T(n,k), n >= 0, 0 <= k <= n, is size of maximal 1-transposition-correcting code formed using binary vectors of length n and weight k.
2

%I #9 Mar 28 2018 22:03:03

%S 1,1,1,1,1,1,1,1,1,1,1,2,2,2,1,1,2,3,3,2,1,1,2,4,6,4,2,1,1,3,6,9,9,6,

%T 3,1,1,3,7,13,15,13,7,3,1,1,3,9,18,24,24,18,9,3,1,1,4,11,24,37,42,37,

%U 24,11,4,1

%N Triangle read by rows: T(n,k), n >= 0, 0 <= k <= n, is size of maximal 1-transposition-correcting code formed using binary vectors of length n and weight k.

%H José Manuel Gómez Soto, Jesús Leaños, Luis Manuel Ríos-Castro, Luis Manuel Rivera, <a href="https://arxiv.org/abs/1711.03682">On an error-correcting code problem</a>, arXiv:1711.03682 [math.CO], 2017.

%H N. J. A. Sloane, <a href="/A265032/a265032.html">Challenge Problems: Independent Sets in Graphs</a>

%e Triangle begins

%e 1

%e 1 1

%e 1 1 1

%e 1 1 1 1

%e 1 2 2 2 1

%e 1 2 3 3 2 1

%e 1 2 4 6 4 2 1

%Y Column k=1 is floor(n/3), column k=2 is A085680, row sums are A057608.

%K nonn,tabl

%O 0,12

%A _N. J. A. Sloane_, Jul 17 2003