Math Is Fun Forum

If we have a matrix with N elements, where each element can take values G ( 0-255), we can obtain  256 power N  possibilities of matrixes ( combinations of elements).

I need to calculate: how many element combinations of the matrix ( no of matrixes) can be obtained with  the same S

You are right about the  matrix, it has 2 variables, x and y, but for simplicity we suppose that we have 1 dimension matrix( a vector) with 1 row and N elements on it.
For example:
for the matrix [1 0 0 2]
S= |0-1|+ |0-0|+ |2-0|=3
f(n0)=1  f(n1)=0 f(n2)=0 and f(n3)=2

Thank you for replying.

I am Sorry for not  using latex.
Maybe you can understand the formula of S in this form:

S = sum (df(n)/d(x))=sum(|f (n+1)- f(n)|)   for n=1,2,3...(N-1)

f(n) is the value of X in the position n of the matrix.

During calculations I have noticed that for S=0 we always get G combinations ( G matrices).
                                                             S=max we always get 2 combinations (matrices)
                                                             S=1 we get  2(N-1)*(G-1)  (matrices)
Now i need to find a formula that gives me the combinations for any S.

I hope this makes the problem more clear for you.