This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369379 #13 Feb 25 2024 10:13:28 %S A369379 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, %T A369379 0,360,0,5,396,0,0,432,0,0,468,0,0,0,0,0,868,0,5,576,0 %N A369379 Number of Dabbaghian-Wu pandiagonal Latin squares of order 2n+1 with the first row in order. %C A369379 A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals. %C A369379 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. %H A369379 Vahid Dabbaghian and Tiankuang Wu, <a href="https://doi.org/10.1016/j.jda.2014.12.001">Constructing non-cyclic pandiagonal Latin squares of prime orders</a>, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001. %H A369379 <a href="https://oeis.org/index/La#Latin">Index entries for sequences related to Latin squares and rectangles</a>. %e A369379 n=13=6*2+1 (prime order): %e A369379 . %e A369379 0 1 2 3 4 5 6 7 8 9 10 11 12 %e A369379 2 3 0 1 11 12 8 4 10 7 5 6 9 %e A369379 4 10 11 2 8 1 3 0 12 6 9 7 5 %e A369379 11 5 9 7 10 0 12 1 3 2 8 4 6 %e A369379 8 7 10 5 9 6 11 2 0 4 3 12 1 %e A369379 12 0 4 6 7 2 9 10 5 11 1 8 3 %e A369379 1 6 12 8 3 4 5 11 9 10 7 2 0 %e A369379 9 2 3 4 12 8 1 6 7 5 0 10 11 %e A369379 10 11 5 0 1 3 7 8 4 12 6 9 2 %e A369379 5 9 1 11 2 10 0 12 6 8 4 3 7 %e A369379 6 8 7 10 0 11 2 9 1 3 12 5 4 %e A369379 7 4 6 12 5 9 10 3 2 0 11 1 8 %e A369379 3 12 8 9 6 7 4 5 11 1 2 0 10 %e A369379 . %e A369379 n=19=6*3+1 (prime order): %e A369379 . %e A369379 0 1 2 3 4 5 6 7 8 9 10 11 12 %e A369379 2 3 0 1 11 12 8 4 10 7 5 6 9 %e A369379 4 10 11 2 8 1 3 0 12 6 9 7 5 %e A369379 11 5 9 7 10 0 12 1 3 2 8 4 6 %e A369379 8 7 10 5 9 6 11 2 0 4 3 12 1 %e A369379 12 0 4 6 7 2 9 10 5 11 1 8 3 %e A369379 1 6 12 8 3 4 5 11 9 10 7 2 0 %e A369379 9 2 3 4 12 8 1 6 7 5 0 10 11 %e A369379 10 11 5 0 1 3 7 8 4 12 6 9 2 %e A369379 5 9 1 11 2 10 0 12 6 8 4 3 7 %e A369379 6 8 7 10 0 11 2 9 1 3 12 5 4 %e A369379 7 4 6 12 5 9 10 3 2 0 11 1 8 %e A369379 3 12 8 9 6 7 4 5 11 1 2 0 10 %e A369379 . %e A369379 n=25=6*4+1 (nonprime order): %e A369379 . %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %e A369379 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 %Y A369379 Cf. A338562, A342306, A368027, A369380. %K A369379 nonn,more %O A369379 1,4 %A A369379 _Eduard I. Vatutin_, Jan 22 2024