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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A369379 Number of Dabbaghian-Wu pandiagonal Latin squares of order 2n+1 with the first row in order. 2
 1, 0, 0, 4, 0, 0, 72, 0, 0, 108, 0, 0, 4, 0, 0, 180, 0, 3, 216, 0, 0, 252, 0, 0, 264, 0, 0, 0, 0, 0, 360, 0, 5, 396, 0, 0, 432, 0, 0, 468, 0, 0, 0, 0, 0, 868, 0, 5, 576, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals. A Dabbaghian-Wu pandiagonal Latin square (see A368027) is a special type of pandiagonal Latin square (see A342306). Such squares are constructed from cyclic diagonal Latin squares (see A338562) for prime orders n=6k+1 (see Dabbaghian and Wu article) using a polynomial algorithm based on permutation of some values in Latin square. For other orders (25, 35, 49, ...) this algorithm also ensures correct pandiagonal Latin squares. LINKS Table of n, a(n) for n=1..50. Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001. Index entries for sequences related to Latin squares and rectangles. EXAMPLE n=13=6*2+1 (prime order): . 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 0 1 11 12 8 4 10 7 5 6 9 4 10 11 2 8 1 3 0 12 6 9 7 5 11 5 9 7 10 0 12 1 3 2 8 4 6 8 7 10 5 9 6 11 2 0 4 3 12 1 12 0 4 6 7 2 9 10 5 11 1 8 3 1 6 12 8 3 4 5 11 9 10 7 2 0 9 2 3 4 12 8 1 6 7 5 0 10 11 10 11 5 0 1 3 7 8 4 12 6 9 2 5 9 1 11 2 10 0 12 6 8 4 3 7 6 8 7 10 0 11 2 9 1 3 12 5 4 7 4 6 12 5 9 10 3 2 0 11 1 8 3 12 8 9 6 7 4 5 11 1 2 0 10 . n=19=6*3+1 (prime order): . 0 1 2 3 4 5 6 7 8 9 10 11 12 2 3 0 1 11 12 8 4 10 7 5 6 9 4 10 11 2 8 1 3 0 12 6 9 7 5 11 5 9 7 10 0 12 1 3 2 8 4 6 8 7 10 5 9 6 11 2 0 4 3 12 1 12 0 4 6 7 2 9 10 5 11 1 8 3 1 6 12 8 3 4 5 11 9 10 7 2 0 9 2 3 4 12 8 1 6 7 5 0 10 11 10 11 5 0 1 3 7 8 4 12 6 9 2 5 9 1 11 2 10 0 12 6 8 4 3 7 6 8 7 10 0 11 2 9 1 3 12 5 4 7 4 6 12 5 9 10 3 2 0 11 1 8 3 12 8 9 6 7 4 5 11 1 2 0 10 . n=25=6*4+1 (nonprime order): . 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3 4 15 6 7 8 9 5 11 12 13 14 0 16 17 18 19 10 21 22 23 24 20 1 2 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 21 22 23 24 5 1 2 3 4 20 9 5 11 12 13 14 10 16 17 18 19 20 21 22 23 24 0 1 2 3 4 15 6 7 8 12 13 14 0 16 17 18 19 10 21 22 23 24 5 1 2 3 4 20 6 7 8 9 15 11 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 18 19 10 21 22 23 24 20 1 2 3 4 15 6 7 8 9 5 11 12 13 14 0 16 17 21 22 23 24 5 1 2 3 4 20 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 24 0 1 2 3 4 15 6 7 8 9 5 11 12 13 14 10 16 17 18 19 20 21 22 23 2 3 4 20 6 7 8 9 15 11 12 13 14 0 16 17 18 19 10 21 22 23 24 5 1 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 8 9 5 11 12 13 14 0 16 17 18 19 10 21 22 23 24 20 1 2 3 4 15 6 7 11 12 13 14 15 16 17 18 19 0 21 22 23 24 5 1 2 3 4 20 6 7 8 9 10 14 10 16 17 18 19 20 21 22 23 24 0 1 2 3 4 15 6 7 8 9 5 11 12 13 17 18 19 10 21 22 23 24 5 1 2 3 4 20 6 7 8 9 15 11 12 13 14 0 16 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 23 24 20 1 2 3 4 15 6 7 8 9 5 11 12 13 14 0 16 17 18 19 10 21 22 1 2 3 4 20 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0 21 22 23 24 5 4 15 6 7 8 9 5 11 12 13 14 10 16 17 18 19 20 21 22 23 24 0 1 2 3 7 8 9 15 11 12 13 14 0 16 17 18 19 10 21 22 23 24 5 1 2 3 4 20 6 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 13 14 0 16 17 18 19 10 21 22 23 24 20 1 2 3 4 15 6 7 8 9 5 11 12 16 17 18 19 0 21 22 23 24 5 1 2 3 4 20 6 7 8 9 10 11 12 13 14 15 19 20 21 22 23 24 0 1 2 3 4 15 6 7 8 9 5 11 12 13 14 10 16 17 18 22 23 24 5 1 2 3 4 20 6 7 8 9 15 11 12 13 14 0 16 17 18 19 10 21 CROSSREFS Cf. A338562, A342306, A368027, A369380. Sequence in context: A192057 A054376 A351156 * A358292 A071608 A013451 Adjacent sequences: A369376 A369377 A369378 * A369380 A369381 A369382 KEYWORD nonn,more AUTHOR Eduard I. Vatutin, Jan 22 2024 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 April 20 17:12 EDT 2024. Contains 371845 sequences. (Running on oeis4.)