word usage - Difference between the use of "a" and "any" in these examples?

I didn't have an idea.

I did not have any idea.

I am much more familiar with the second one. The first one sounds a bit odd to me, but sounds fine if I say:

I did not have even an idea.

But, the first one is also one of the widely used sentences by natives. What is the difference between the two?

Answer

I did not have an idea = I was asked to contribute an idea but I was unable to think of one; an idea did not come into my head in some situation where an idea was expected from me.

I had no idea = I was unable to explain something; it was a mystery to me or it was something about which I had no knowledge whatsoever.

I did not have any idea = I had no idea.