function a = antisummation_inverse ( n )

%*****************************************************************************80
%
%% antisummation_inverse() returns the inverse of the ANTISUMMATION matrix.
%
%  Example:
%
%    N = 5
%
%    1  0  0  0  0
%    1  1  0  0  0
%    2  1  1  0  0
%    4  2  1  1  0
%    8  4  2  1  1
%
%  Properties:
%
%    A is lower triangular.
%
%    A is Toeplitz: constant along diagonals.
%
%    A is nonsingular.
%
%    det ( A ) = 1.
%
%    A is the inverse of the antisummation matrix.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    14 October 2022
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    integer N, the order of the matrix.
%
%  Output:
%
%    real A(N,N), the matrix.
%
  a = zeros ( n, n );

  for i = 1 : n
    for j = 1 : n
      if ( i == j )
        a(i,j) = 1.0;
      elseif ( j < i )
        a(i,j) = 2.0 ^ ( i - j - 1 );
      else
        a(i,j) = 0.0;
      end
    end
  end

  return
end
