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

Author

Eduard I. Vatutin, Feb 15 2024

Keywords

• nonn
• more
• hard

Comments

a(9)>=64, a(10)>=103, a(11)>=145, a(12)>=259, a(13)>=200, 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)>=1679, a(26)>=2040, a(28)>=2803. - Eduard I. Vatutin, added Aug 13 2024, updated Jun 25 2025

Examples

			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.
		

Links

• 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).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A092237, A309344, A345760.