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 A343868 #14 May 24 2021 23:31:27 %S A343868 0,0,0,8,40,338,1512,11368,84960,828972,7291900,85823668,958954152, %T A343868 12930529446,176651211776,2631044069296,41847091313152 %N A343868 Number of semicyclic Latin squares of order n with the first row in ascending order. %C A343868 A semicyclic Latin square is cyclic in one or more directions but not in every direction. Cyclic Latin squares which are cyclic in essentially every direction are excluded. A direction here means any constant row and column displacement on the torus. See the reference in A343867 for additional information. %C A343868 Each symbol occupies the same pattern of squares up to translation on the torus. %H A343868 Andrew Howroyd, <a href="/A343868/a343868.txt">Order 6 semicyclic Latin squares</a> %H A343868 Andrew Howroyd, <a href="/A343868/a343868_1.txt">PARI Program</a> %F A343868 a(n) >= 2*((n-1)! - phi(n)). %F A343868 a(p) = 2*(p-1)! + (p-1)*(A003111((p-1)/2) - p) for odd prime p. %e A343868 The permutation 164253 can be shown in a 6 X 6 grid: %e A343868 X . . . . . %e A343868 . . . . . X %e A343868 . . . X . . %e A343868 . X . . . . %e A343868 . . . . X . %e A343868 . . X . . . %e A343868 This permutation gives the following 4 semicyclic squares. %e A343868 1 2 3 4 5 6 1 4 2 5 3 6 1 4 3 6 2 5 1 4 5 2 3 6 %e A343868 2 3 4 5 6 1 2 5 3 6 4 1 3 6 2 5 4 1 2 5 6 3 4 1 %e A343868 4 5 6 1 2 3 3 6 4 1 5 2 5 2 4 1 3 6 6 3 4 1 2 5 %e A343868 6 1 2 3 4 5 4 1 5 2 6 3 4 1 6 3 5 2 4 1 2 5 6 3 %e A343868 3 4 5 6 1 2 5 2 6 3 1 4 6 3 5 2 1 4 5 2 3 6 1 4 %e A343868 5 6 1 2 3 4 6 3 1 4 2 5 2 5 1 4 6 3 3 6 1 4 5 2 %e A343868 In the third example, moving one cell down and two across increases the cell value by 1 (cyclically) and in the fourth example the displacement is 3 rows down and 2 across. Symbols can then be rearranged to give 4 distinct semicyclic squares with the first row in ascending order. %o A343868 (PARI) \\ See Links %Y A343868 Cf. A000010 (phi), A001615, A003111, A343867. %K A343868 nonn,more %O A343868 1,4 %A A343868 _Andrew Howroyd_, May 08 2021