A362649 Number of nonisomorphic unordered pairs of involutions on an n-set.

1, 1, 3, 4, 10, 13, 27, 36, 69, 92, 162, 217, 365, 487, 782, 1043, 1622, 2154, 3253, 4306, 6355, 8376, 12107, 15893, 22582, 29512, 41285, 53729, 74164, 96100, 131054, 169110, 228165, 293202, 391752, 501406, 664093, 846642, 1112363, 1412768, 1842620

Offset

0,3

Comments

Isomorphism is up to permutation of the elements of the n-set.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Example

The a(4)=10 pairs of involutions are:
  {(), ()},
  {(), (34)},
  {(), (12)(34)},
  {(34), (34)},
  {(34), (23)},
  {(34), (12)},
  {(34), (12)(34)},
  {(34), (13)(24)},
  {(12)(34), (12)(34)},
  {(12)(34), (13)(24)}.

Crossrefs

Column k=2 of A362648.

Cf. A000085, A362645.

Sequence in context: A257494 A302347 A092119 * A143372 A035594 A167273

Adjacent sequences: A362646 A362647 A362648 * A362650 A362651 A362652

Keyword

nonn

Author

Andrew Howroyd, May 01 2023

Status

approved