My idea is as follows: the tensor has 4^4 = 256 components --> calculate all zero components N --> (256 - N)/2^6 should be one, as 4 unequal indices can be arranged in 6 ways, so that every arrangements cuts the number of independent components in half.

I believe this is correct, but correct me if I am wrong. The tricky part is calculating the number N. My idea: N = #(2 indices equal) + #(3 indices equal) + #(4 equal).

Obviously: #(4 equal) = 4 and #(3 equal) = 4*4*3 = 48. Then:

#(2 indices equal) = #(2 equal, other two equal) + #(2 equal, other not equal) = 36 + 12*4*3*2*0.5 = 180.

This would yield N = 180 + 4 + 36 = 232, which is obviously not correct.

Can anyone help me? Thanks in advance!