function a = delannoy ( m, n )

%*****************************************************************************80
%
%% DELANNOY returns the Delannoy numbers up to orders (M,N).
%
%  Discussion:
%
%    The Delannoy number A(M,N) counts the number of distinct paths
%    from (0,0) to (M,N) in which the only steps used are
%    (1,1), (1,0) and (0,1).
%
%  First values:
%
%      \N 0  1   2   3    4     5     6      7      8
%     M-+--------------------------------------------
%     0 : 1  1   1   1    1     1     1      1      1
%     1 : 1  3   5   7    9    11    13     15     17
%     2 : 1  5  13  25   41    61    85    113    145
%     3 : 1  7  25  63  129   231   377    575    833
%     4 : 1  9  41 129  321   681  1289   2241   3649
%     5 : 1 11  61 231  681  1683  3653   7183  13073
%     6 : 1 13  85 377 1289  3653  8989  19825  40081
%     7 : 1 15 113 575 2241  7183 19825  48639 108545
%     8 : 1 17 145 833 3649 13073 40081 108545 265729
%
%  Recursion:
%
%    A(0,0) = 1
%    A(M,0) = 1
%    A(0,N) = 1
%    A(M,N) = A(M-1,N) + A(M,N-1) + A(M-1,N-1)
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    26 July 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Eric Weisstein
%    CRC Concise Encyclopedia of Mathematics,
%    CRC Press, 1998
%
%  Parameters:
%
%    Input, integer M, N, define the highest order number to compute.
%
%    Output, integer A(1:M+1,1:N+1), the Delannoy numbers.
%
  if ( m < 0 )
    a = [];
    return
  end

  if ( n < 0 )
    a = [];
    return
  end

  a = zeros ( m + 1, n + 1 );

  a(1,1) = 1;

  a(2:m+1,1) = 1;
  a(1,2:n+1) = 1;

  for i = 1 : m
    for j = 1 : n
      a(i+1,j+1) = a(i,j+1) + a(i+1,j) + a(i,j);
    end
  end

  return
end