The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A345370 a(n) is the number of distinct numbers of diagonal transversals that a diagonal Latin square of order n can have. 7
 1, 0, 0, 1, 2, 2, 14, 47, 182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n) <= A287648(n) - A287647(n) + 1. a(n) <= A287764(n). Conjecture: a(12) = A287648(12) - A287647(12) + 1. - Natalia Makarova, Oct 26 2021 a(10) >= 736, a(11) >= 1242, a(12) >= 17693, a(13) >= 14017, a(14) >= 281067, a(15) >= 1958394, a(16) >= 13715. - Eduard I. Vatutin, Oct 29 2021, updated May 14 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, On the falsity of conjecture that spectra of diagonal transversals for diagonal Latin squares of order 12 is solid (in Russian). Eduard I. Vatutin, Graphical representation of the spectra. 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, Proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12). E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021). Tula, 2021. pp. 7-17. (in Russian) 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 diagonal transversals that a diagonal Latin square of order 7 may have is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, or 27. Since there are 14 distinct values, a(7)=14. CROSSREFS Cf. A287647, A287648, A309344, A344105, A345760, A345761, A349199. Sequence in context: A194689 A277556 A321179 * A166114 A202730 A292080 Adjacent sequences: A345367 A345368 A345369 * A345371 A345372 A345373 KEYWORD nonn,more,hard AUTHOR Eduard I. Vatutin, Jun 16 2021 EXTENSIONS a(8) added by Eduard I. Vatutin, Jul 15 2021 a(9) added by Eduard I. Vatutin, Oct 20 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 29 02:45 EDT 2023. Contains 365749 sequences. (Running on oeis4.)