A085684 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.

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, 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, 24, 11, 4, 1

Offset

0,12

Links

Table of n, a(n) for n=0..65.

José Manuel Gómez Soto, Jesús Leaños, Luis Manuel Ríos-Castro, Luis Manuel Rivera, On an error-correcting code problem, arXiv:1711.03682 [math.CO], 2017.

N. J. A. Sloane, Challenge Problems: Independent Sets in Graphs

Example

Triangle begins
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

Crossrefs

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

Sequence in context: A245421 A134143 A295555 * A141604 A143996 A301562

Adjacent sequences: A085681 A085682 A085683 * A085685 A085686 A085687

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jul 17 2003

Status

approved