A345760 a(n) is the number of distinct numbers of intercalates of order n diagonal Latin squares.

0, 0, 0, 1, 2, 1, 21, 61, 64

Offset

1,5

Comments

a(n) <= A307164(n) - A307163(n) + 1.

a(n) <= A287764(n).

a(10) >= 98, a(11) >= 145, a(12) >= 259, a(13) >= 197, a(14) >= 362, a(15) >= 536, a(16) >= 789, a(17) >= 685, a(18) >= 419, a(19) >= 447, a(20) >= 1009, a(21) >= 740, a(22) >= 737, a(23) >= 885, a(24) >= 1610. - Eduard I. Vatutin, Oct 02 2021, updated May 21 2023

Links

Table of n, a(n) for n=1..9.

Eduard I. Vatutin, About the spectra of numerical characteristics of diagonal Latin squares of orders 1-7 (in Russian).

Eduard I. Vatutin, About the spectra of numerical characteristics of diagonal Latin squares of order 8 (in Russian).

Eduard I. Vatutin, About the approximation of spectra of numerical characteristics of diagonal Latin squares of order 9 (in Russian).

Eduard I. Vatutin, About the results of experiment with spectra of diagonal Latin squares using Brute Force and distributed computing projects Gerasim@Home and RakeSearch (in Russian).

Eduard I. Vatutin, Graphical representation of the spectra.

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

E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, I. I. Kurochkin, A. M. Albertyan, A. V. Kripachev, A. I. Pykhtin, Methods for getting spectra of fast computable numerical characteristics of diagonal Latin squares, Cloud and distributed computing systems in electronic control conference, within the National supercomputing forum (NSCF - 2022). Pereslavl-Zalessky, 2023. pp. 19-23. (in Russian)

E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan and I. I. Kurochkin, Estimation of the Cardinalities of the Spectra of Fast-computable Numerical Characteristics for Diagonal Latin Squares of Orders N>9 (in Russian) // Science and education in the development of industrial, social and economic spheres of Russian regions. Murom, 2022. pp. 314-315.

E. I. Vatutin, V. S. Titov, A. I. Pykhtin, A. V. Kripachev, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, I. I. Kurochkin, Heuristic method for getting approximations of spectra of numerical characteristics for diagonal Latin squares, Intellectual information systems: trends, problems, prospects, Kursk, 2022. pp. 35-41. (in Russian)

Index entries for sequences related to Latin squares and rectangles.

Example

For n=7 the number of intercalates that a diagonal Latin square of order 7 may have is 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 26, or 30. Since there are 21 distinct values, a(7)=21.

Crossrefs

Cf. A287764, A307163, A307164, A309344, A344105, A345370, A345761.

Sequence in context: A051492 A380220 A164827 * A213976 A330354 A200859

Adjacent sequences: A345757 A345758 A345759 * A345761 A345762 A345763

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jun 26 2021

Extensions

a(9) added by Eduard I. Vatutin, Oct 22 2022

Status

approved