A226522 Irregular triangle read by rows: T(n,k) = maximal number of minimal codewords over the set of all [n,k] cycle codes, for n >= 3.

1, 1, 1, 3, 1, 3, 7, 1, 3, 7, 1, 3, 7, 13, 1, 3, 7, 15, 22, 1, 3, 7, 15, 24, 37, 1, 3, 7, 15, 26, 39, 1, 3, 7, 15, 29, 42, 63, 1, 3, 7, 15, 29, 46, 69, 91, 1, 3, 7, 15, 29, 51, 75, 108, 133, 1, 3, 7, 15, 29, 57, 82, 123, 156, 197

Offset

3,4

Comments

"Cycle code" refers to the linear code generated by the cycles of a connected graph.

Links

Table of n, a(n) for n=3..67.

A. Alahmadi, R. E. L. Aldred, R. dela Cruz, P. Solé, C. Thomassen, The maximum number of minimal codewords in an [n,k]-code, arXiv:1203.0728v1 [cs.IT], Mar 4, 2012.

A. Alahmadi, R. E. L. Aldred, R. dela Cruz, P. Solé, C. Thomassen, The maximum number of minimal codewords in an [n,k]-code, Discrete Math., 313 (2013), 1569-1574. (This triangle is not part of the version of this paper on the arXiv.)

Example

Triangle begins:
1
1
1 3
1 3 7
1 3 7
1 3 7 13
1 3 7 15 22
1 3 7 15 24 37
1 3 7 15 26 39
1 3 7 15 29 42 63
1 3 7 15 29 46 69 91
1 3 7 15 29 51 75 108 133
1 3 7 15 29 57 82 123 156 197
...

Crossrefs

Cf. A209334.

Sequence in context: A205121 A152903 A377342 * A122507 A257258 A259325

Adjacent sequences: A226519 A226520 A226521 * A226523 A226524 A226525

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 20 2013

Status

approved