cp's OEIS Frontend

An intercalate is a 2 X 2 subsquare of a Latin square.

Every diagonal Latin square is a Latin square, so 0 <= a(n) <= A307164(n) <= A092237(n). - Eduard I. Vatutin, Sep 21 2020

Every intercalate is a partial loop and every partial loop is a loop, so 0 <= a(n) <= A307170(n) <= A307166(n). - Eduard I. Vatutin, Oct 19 2020

a(n)=0 for all orders n for which cyclic diagonal Latin squares exist (see A007310) due to all cyclic diagonal Latin squares don't have intercalates. - Eduard I. Vatutin, Aug 07 2023

a(n)=0 for all orders n for which diagonalized cyclic diagonal Latin squares exist (see A372922) due to all diagonalized cyclic diagonal Latin squares don't have intercalates. - Eduard I. Vatutin, Sep 24 2024

a(16) <= 2, a(17) = 0, a(18) <= 9, a(19) = 0, a(20) <= 1, a(21) <= 11, a(22) <= 9, a(23) = 0, a(24) <= 16, a(25) = 0, a(26) <= 29. - Eduard I. Vatutin, added Sep 10 2023, updated Mar 01 2025

See Comments in A372922.

Diagonalized cyclic diagonal Latin squares are diagonal Latin squares that are isomorphic to cyclic Latin squares. They are can be obtained from cyclic Latin squares (see A338522) by diagonalization (getting a corresponding pair of transversals and placing them on the diagonals, see article). Diagonalized cyclic diagonal Latin squares have some interesting properties, for example, there are a large number of diagonal transversals for diagonal Latin squares of odd orders.