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I suppose this is the formula for min. no. of processes required for deadlock. For this, we assume the worst case and this happens when all but 1 required resources are taken by all the processes.

i.e., total allocated = total max need - n  

If we have one more resource, one process can be finished and this results in more processes getting finished and there won't be a deadlock. So, for deadlock,  

max. no. of resources = total max. need - n

or

total max. need = n + no. of resources

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