A232225 Irregular triangle read by rows: T(n,k) = number of crossing connected diagrams in a disk having n crossings and k vertices.

1, 0, 5, 3, 0, 5, 31, 35, 12, 0, 0, 54, 231, 346, 225, 55, 0, 1, 51, 532, 1942, 3366, 3062, 1430, 273, 0, 0, 39, 784, 5253, 17631, 33300, 37312, 24804, 9100, 1428

Offset

1,3

Links

Table of n, a(n) for n=1..36.

V. Pilaud and J. Rué, Analytic combinatorics of chord and hyperchord diagrams with k crossings, arXiv preprint arXiv:1307.6440 [math.CO], 2013.

Example

Triangle begins:
  1;
  0, 5,  3;
  0, 5, 31,  35,   12;
  0, 0, 54, 231,  346,   225,    55;
  0, 1, 51, 532, 1942,  3366,  3062,  1430,   273;
  0, 0, 39, 784, 5253, 17631, 33300, 37312, 24804, 9100, 1428;
  ...

Crossrefs

Cf. A232226 (row sums), A232227.

Sequence in context: A144481 A374172 A350550 * A365075 A200126 A065469

Adjacent sequences: A232222 A232223 A232224 * A232226 A232227 A232228

Keyword

nonn,tabf,more

Author

N. J. A. Sloane, Nov 22 2013

Status

approved