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A109741 Number of inequivalent (completed) n^2 X n^2 sudokus (or Sudokus).

%I A109741 #24 Feb 16 2025 08:32:58
%S A109741 1,1,2,5472730538
%N A109741 Number of inequivalent (completed) n^2 X n^2 sudokus (or Sudokus).
%C A109741 See A107739 for definition of an n^2 X n^2 sudoku.
%C A109741 a(2) = 2 independently computed by Gary McGuire and _Hugo van der Sanden_.
%C A109741 For the 9 X 9 case the allowed equivalences are (see link to Jarvis et al.):
%C A109741 - relabeling entries; reflection; rotation;
%C A109741 - permutation of blocks of columns 1-3, 4-6 and 7-9;
%C A109741 - permutation of blocks of rows 1-3, 4-6 and 7-9;
%C A109741 - permutation of columns 1-3; permutation of rows 1-3;
%C A109741 - permutation of columns 4-6; permutation of rows 4-6;
%C A109741 - permutation of columns 7-9; permutation of rows 7-9.
%C A109741 See A107739 for the total number of ("square") sudoku grids, A114288 for the lexicographically earliest 9 X 9 solution. - _M. F. Hasler_, Mar 29 2013
%D A109741 J.-P. Delahaye, "Le tsunami du Sudoku" in 'Pour La Science' (French Edition of "Scientific American"), December 2005 pp. 144-9, Paris.
%H A109741 J. P. Grossman, <a href="http://www.mathstat.dal.ca/~jpg/sudoku/">Javascript Sudoku solver</a>
%H A109741 S. Gupta, <a href="http://theory.tifr.res.in/~sgupta/sudoku/challenges.html#prime">Exploring the Mathematics of Su Doku</a>
%H A109741 Frazer Jarvis et al., <a href="https://web.archive.org/web/20220305080012/http://www.afjarvis.staff.shef.ac.uk/sudoku/">Sudoku enumeration problems</a>
%H A109741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sudoku.html">Sudoku</a>
%H A109741 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sudoku">Sudoku</a>
%e A109741 a(2) = 2:
%e A109741 12|34 12|34
%e A109741 34|12 34|12
%e A109741 --+-- --+--
%e A109741 21|43 23|41
%e A109741 43|21 41|23
%K A109741 nonn,bref,hard
%O A109741 0,3
%A A109741 _N. J. A. Sloane_, Aug 13 2005
%E A109741 Links to Jarvis et al. fixed by _M. F. Hasler_, Mar 29 2013