function number = comp_enum ( n, k )
%*****************************************************************************80
%
%% comp_enum() returns the number of compositions of the integer N into K parts.
%
% Discussion:
%
% A composition of the integer N into K parts is an ordered sequence
% of K nonnegative integers which sum to N. The compositions (1,2,1)
% and (1,1,2) are considered to be distinct.
%
% The 28 compositions of 6 into three parts are:
%
% 6 0 0, 5 1 0, 5 0 1, 4 2 0, 4 1 1, 4 0 2,
% 3 3 0, 3 2 1, 3 1 2, 3 0 3, 2 4 0, 2 3 1,
% 2 2 2, 2 1 3, 2 0 4, 1 5 0, 1 4 1, 1 3 2,
% 1 2 3, 1 1 4, 1 0 5, 0 6 0, 0 5 1, 0 4 2,
% 0 3 3, 0 2 4, 0 1 5, 0 0 6.
%
% The formula for the number of compositions of N into K parts is
%
% Number = ( N + K - 1 )! / ( N! * ( K - 1 )! )
%
% Describe the composition using N '1's and K-1 dividing lines '|'.
% The number of distinct permutations of these symbols is the number
% of compositions. This is equal to the number of permutations of
% N+K-1 things, with N identical of one kind and K-1 identical of another.
%
% Thus, for the above example, we have:
%
% Number = ( 6 + 3 - 1 )! / ( 6! * (3-1)! ) = 28
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 11 January 2021
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Albert Nijenhuis, Herbert Wilf,
% Combinatorial Algorithms for Computers and Calculators,
% Second Edition,
% Academic Press, 1978,
% ISBN: 0-12-519260-6,
% LC: QA164.N54.
%
% Input:
%
% integer N, the integer whose compositions are desired.
%
% integer K, the number of parts in the composition.
%
% Output:
%
% integer NUMBER, the number of compositions of N into K parts.
%
number = nchoosek ( n + k - 1, n );
return
end