What the OP is calculating is the number of bit pairing (4 values) for each combination of 2 strings.

Eg: Assuming 32-bit strings, typical values might be: 

strings: '00'   '01'    '10'    '11'
1 & 2     10      5      12      15
1 & 3      2     17       7       6
1 & 4    
1 & 5 
2 & 3 ....

[download]

So the OP wants 4 numbers per pairing of strings, regardless of the number of bits.

What you would be calculating is 4 numbers per bit position, regardless of the number of strings.

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In reply to Re^6: Speeding permutation counting by BrowserUk
in thread Speeding permutation counting by albert

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