% Permutations of 1 2 3 4 5 in lexicographical order:
A = sortrows( perms(1:5) );
 
% In reverse lexicographical order:
B = rot90(A,2);
 

whos
  Name        Size            Bytes  Class     Attributes
 
  A         120x5              4800  double              
  B         120x5              4800  double              
 

% Add the integers from 6 to 120 to each row,
% which are not changed in their position by the permutations:

for k=1:120
C(k,1:115)=[6:120];
end    


whos C
  Name        Size              Bytes  Class     Attributes
 
  C         120x115            110400  double              
 

D = cell2mat( { B C } );  
 

whos D
  Name        Size              Bytes  Class     Attributes
 
  D         120x120            115200  double              
 

% Reflect the square matrix, to calculate the diagonals:
E = rot90(D)';
 
% Calculate the diagonals:
for k=1:120
X(((k^2-k)/2+1):((k^2+k)/2)) = diag(E,120-k);
end


whos X
  Name      Size              Bytes  Class     Attributes
 
  X         1x7260            58080  double              
 






% Show first 55 enries of the sequence X:

X(1:55)
ans =
  Columns 1 through 10
     1     2     2     3     1     1     4     3     3     3
  Columns 11 through 20
     5     4     2     1     2     6     5     4     2     3
  Columns 21 through 30
     3     7     6     5     4     1     2     1     8     7
  Columns 31 through 40
     6     5     4     1     2     2     9     8     7     6
  Columns 41 through 50
     5     4     4     1     1    10     9     8     7     6
  Columns 51 through 55
     5     3     4     4     4







% These are the first 10 antidiagonals of the square matrix D:

X(1)
ans =
     1
X(2:3)
ans =
     2     2
X(4:6)
ans =
     3     1     1
X(7:10)
ans =
     4     3     3     3
X(11:15)
ans =
     5     4     2     1     2
X(16:21)
ans =
     6     5     4     2     3     3
X(22:28)
ans =
     7     6     5     4     1     2     1
X(29:36)
ans =
     8     7     6     5     4     1     2     2
X(37:45)
ans =
     9     8     7     6     5     4     4     1     1
X(46:55)
ans =
    10     9     8     7     6     5     3     4     4     4