A350017 Number of isotopism classes containing symmetric unipotent reduced Latin squares of order 2n.

1, 1, 1, 6, 396, 526915616, 1132835421602062347

Offset: 1

Author

Ian Wanless, Dec 08 2021

Keywords

• nonn
• more

Comments

Isotopism classes are obtained by permuting rows, permuting columns and permuting symbols. There is a stronger notion of equivalence called "species" (also known as main classes and paratopism classes). For this particular problem the counts for species equal the counts for isotopism classes.

Links

• Brendan D. McKay and Ian M. Wanless, Enumeration of Latin squares with conjugate symmetry, J. Combin. Des. 30 (2022), 105-130.

Crossrefs

For odd n the terms equal A000474.

Cf. A350009.