A368182 a(n) is the number of distinct numbers of intercalates in Latin squares of order n.

1, 1, 1, 2, 2, 9, 23, 61

Offset

1,4

Comments

a(9)>=64, a(10)>=103, a(11)>=145, a(12)>=259, a(13)>=212, a(14)>=362, a(15)>=536, a(16)>=794, a(17)>=705, a(18)>=655, a(19)>=469, a(20)>=1362, a(21)>=985, a(22)>=1435, a(23)>=967, a(24)>=1754, a(25)>=1869, a(26)>=2040, a(28)>=2803. - Eduard I. Vatutin, added Aug 13 2024, updated Sep 24 2025

Links

Table of n, a(n) for n=1..8.

Eduard I. Vatutin, About the intercalates spectra in a Latin squares of orders 1-8 (in Russian).

Eduard I. Vatutin, Graphical representation of the spectra.

Eduard I. Vatutin, Proving lists (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28).

Eduard Vatutin, Jia Wei-Ting, Jun Chi Ma, Qiang Miao, Maxim Manzyuk, Natalia Kukushkina, Ilya Kurochkin, and Alexander Albertian, Construction of Intercalate Number Spectra in Latin Squares of Orders 18-28 Using Distributed Parallel Software Implementations, Supercomputing (RuSCDays 2025) 462-474. See references.

Index entries for sequences related to Latin squares and rectangles.

Example

For n=7, a Latin square of order 7 may have 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 26, 30, or 42 intercalates. There are 23 possibilities, so a(7)=23.

Crossrefs

Cf. A092237, A309344, A345760.

Sequence in context: A180753 A389631 A220971 * A363451 A369076 A308519

Adjacent sequences: A368179 A368180 A368181 * A368183 A368184 A368185

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Feb 15 2024

Status

approved