function value = i4_partition_distinct_count ( n )
%*****************************************************************************80
%
%% I4_PARTITION_DISTINCT_COUNT returns any value of Q(N).
%
% Discussion:
%
% A partition of an integer N is a representation of the integer
% as the sum of nonzero positive integers. The order of the summands
% does not matter. The number of partitions of N is symbolized
% by P(N). Thus, the number 5 has P(N) = 7, because it has the
% following partitions:
%
% 5 = 5
% = 4 + 1
% = 3 + 2
% = 3 + 1 + 1
% = 2 + 2 + 1
% = 2 + 1 + 1 + 1
% = 1 + 1 + 1 + 1 + 1
%
% However, if we require that each member of the partition
% be distinct, we are computing something symbolized by Q(N).
% The number 5 has Q(N) = 3, because it has the following partitions
% into distinct parts:
%
% 5 = 5
% = 4 + 1
% = 3 + 2
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 27 July 2004
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Milton Abramowitz and Irene Stegun,
% Handbook of Mathematical Functions,
% US Department of Commerce, 1964.
%
% Input:
%
% integer N, the integer to be partitioned.
%
% Output:
%
% integer VALUE, the number of partitions of the integer
% into distinct parts.
%
c(1) = 1;
for i = 1 : n
if ( i4_is_triangular ( i ) )
c(i+1) = 1;
else
c(i+1) = 0;
end
k = 0;
k_sign = -1;
while ( true )
k = k + 1;
k_sign = - k_sign;
k2 = k * ( 3 * k + 1 );
if ( i < k2 )
break
end
c(i+1) = c(i+1) + k_sign * c(i-k2+1);
end
k = 0;
k_sign = -1;
while ( true )
k = k + 1;
k_sign = -k_sign;
k2 = k * ( 3 * k - 1 );
if ( i < k2 )
break
end
c(i+1) = c(i+1) + k_sign * c(i-k2+1);
end
end
value = c(n+1);
return
end