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 A309344 a(n) is the number of distinct numbers of transversals of order n Latin squares. 0
 1, 1, 1, 2, 2, 4, 36, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS We found all transversals in the main class Latin square representatives of order n. These results are based upon work supported by the National Science Foundation under the grants numbered DMS-1852378 and DMS-1560019. LINKS Brendan McKay, Combinatorial Data EXAMPLE For n=7, the number of transversals that an order 7 Latin square may have is 3, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 41, 43, 45, 47, 55, 63, or 133. Hence there are 36 distinct numbers of transversals of order 7 Latin squares, so a(7)=36. PROG (MATLAB) %This extracts entries from each column.  For an example, if %A=[1 2 3 4; 5 6 7 8; 9 10 11 12; 13 14 15 16], and if list = (2, 1, 4), %this code extracts the second element in the first column, the first %element in the second column, and the fourth element in the third column. function [output] = extract(matrix, list) for i=1:length(list)     output(i) = matrix(list(i), i); end end %Searches matrix to find transversal and outputs the transversal. function [output] = findtransversal(matrix) n=length(matrix); for i=1:n     partialtransversal(i, 1)=i; end for i=2:n     newpartialtransversal=[];     for j=1:length(partialtransversal)         for k=1:n             if (~ismember(k, partialtransversal(j, :)))&(~ismember(matrix(k, i), extract(matrix, partialtransversal(j, :))))                 newpartialtransversal=[newpartialtransversal; [partialtransversal(j, :), k]];             end         end     end     partialtransversal=newpartialtransversal; end output=partialtransversal; end %Takes input of n^2 numbers with no spaces between them and converts it %into an n by n matrix. function [A] = tomatrix(input) n=sqrt(floor(log10(input))+2); for i=1:n^2     temp(i)=mod(floor(input/(10^(i-1))), 10); end for i=1:n     for j=1:n         A(i, j)=temp(n^2+1-(n*(i-1)+j));     end end A=A+ones(n); end CROSSREFS Cf. A301371, A308853, A309088. Sequence in context: A327011 A300361 A257617 * A257618 A088895 A257619 Adjacent sequences:  A309341 A309342 A309343 * A309345 A309346 A309347 KEYWORD nonn,hard,more AUTHOR STATUS approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)