function [ n_data, order, number ] = polyomino_fixed_count_values ( n_data )

%*****************************************************************************80
%
%% polyomino_fixed_count_values() counts fixed polyominoes (allowing holes).
%
%  Discussion:
%
%    Polyominoes are connected planar shapes formed by adjoining unit squares.
%
%    The number of unit squares in a polyomino is its order.
%
%    If we do not ignore reflections and rotations when comparing polyominoes,
%    then we are considering the class of "fixed" polyominoes.  In that case,
%    for instance, there are 65 fixed polyominoes of order 5.
%
%    As the order increases, the number of polyominoes grows very rapidly.
%    The list offered here goes no further than order 28, but the later
%    numbers in the list are too large to represent as 32 byte integers. 
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    10 April 2018
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Solomon Golomb,
%    Polyominoes: Puzzles, Patterns, Problems, and Packings,
%    Princeton University Press, 1996,
%    ISBN: 9780691024448
%
%  Input:
%
%    integer N_DATA.  The user sets N_DATA to 0 before the first call.  
%    Thereafter, it should simply be the value returned by the previous call.
%
%  Output:
%
%    integer N_DATA.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    integer ORDER, the order of a polyomino.
%
%    integer NUMBER, the number of fixed polyominos of this order.
%
  n_max = 29;

  order_vec = [ ...
    0, ...
    1,  2,  3,  4,  5, ...
    6,  7,  8,  9, 10, ...
   11, 12, 13, 14, 15, ...
   16, 17, 18, 19, 20, ...
   21, 22, 23, 24, 25, ...
   26, 27, 28 ];

  number_vec = [  ...
    1, ...
    1, 2, 6, 19, 63,  ...
    216, 760, 2725, 9910, 36446,  ...
    135268, 505861, 1903890, 7204874, 27394666,  ...
    104592937, 400795844, 1540820542, 5940738676, 22964779660,  ...
    88983512783, 345532572678, 1344372335524, 5239988770268, 20457802016011,  ...
    79992676367108, 313224032098244, 1228088671826973 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    order = 0;
    number = 0;
  else
    order = order_vec(n_data);
    number = number_vec(n_data);
  end

  return
end
