A293176 Irregular triangle read by rows: T(n,k) = number of numerical semigroups of genus n with k even gaps.

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 2, 6, 3, 1, 2, 7, 12, 1, 1, 2, 7, 19, 10, 1, 2, 7, 21, 32, 4, 1, 2, 7, 23, 51, 33, 1, 1, 2, 7, 23, 62, 91, 18, 1, 2, 7, 23, 65, 142, 98, 5, 1, 2, 7, 23, 68, 174, 257, 59, 1, 1, 2, 7, 23, 68, 192, 412, 271, 25, 1, 2, 7, 23, 68, 197, 514, 678, 197, 6

Offset

0,6

Links

Table of n, a(n) for n=0..79.

M. Bernardini, Fernando Torres. "Counting numerical semigroups by genus and even gaps." Discrete Mathematics 340.12 (2017): 2853-2863. Also arXiv:1612.01212.

Example

Triangle begins:
1,
1,
1,1,
1,2,1,
1,2,4,
1,2,6,3,
1,2,7,12,1,
1,2,7,19,10,
1,2,7,21,32,4,
1,2,7,23,51,33,1,
1,2,7,23,62,91,18,
1,2,7,23,65,142,98,5,
1,2,7,23,68,174,257,59,1,
1,2,7,23,68,192,412,271,25,
1,2,7,23,68,197,514,678,197,6,
...

Crossrefs

Cf. A007323 (row sums).

Sequence in context: A056061 A029265 A103648 * A297170 A359627 A127309

Adjacent sequences: A293173 A293174 A293175 * A293177 A293178 A293179

Keyword

nonn,tabf,changed

Author

N. J. A. Sloane, Oct 19 2017

Status

approved