A350009 a(n) is the number of isotopism classes containing symmetric Latin squares of order n.

1, 1, 1, 2, 1, 6, 7, 415, 3460, 35878418, 6320290037, 4612965997149292, 15859695832489637513

Offset

1,4

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

Table of n, a(n) for n=1..13.

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

Crossrefs

The odd terms agree with A350010. Cf. A035481

Sequence in context: A243320 A363470 A319897 * A350010 A193734 A379460

Adjacent sequences: A350006 A350007 A350008 * A350010 A350011 A350012

Keyword

nonn,more

Author

Ian Wanless, Dec 08 2021

Status

approved