How to calculate the total number of incidences of a kj part in all compositions of a natural number N
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A composition of natural number N is a partition in ki summands(parts) of N=k1+k2+k3+k4...+ki , with ki >or =1 and ki<N, where the order of the parts is important. For instance there are 3 compositions of N=3 are: {1,1,1} {1,2} {2,1}
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Kaitlyn Keil
on 27 Jul 2018
Here is a loop that will print this out for you, though it does include the single case (just the number itself):
function count = countAllCombinators(arr, n)
if n==0
disp(arr);
count = 1;
elseif(n > 0)
count = 0;
for k = 1:n
subarr = [arr k];
count = count + countAllCombinators(subarr, n-k);
end
end
end
Hope that helps!
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