Is the census by David in the book of 2Samuel and 1Chronicles described contradictorily? 

2 Sam. 24:1 'Again the Lord kindled wrath against Israel. He set David against the people, saying, 'Go and take a census in Israel and Judah.'

1 Chron. 21:1 "Satan turned against Israel and prompted David to take a census in Israel.

Sometimes God takes initiative, other times Satan. A contradiction? First, one can understand the Hebrew satan in 1 Chronicles also translate with "adversary," which is often the correct translation in the OT. In that case, this would refer to a foreign enemy pressuring David to take a census. And in 2 Samuel Is it possible to translate, "Again the Lord kindled wrath against Israel. Someone pitted David against the people ...

But then still remains here that in 2 Samuel God takes the initiative and in 1 Chronicles Satan or a human enemy. But two authors (God and Satan) of the same event are very common in a spiritual sense. Satan executes what God allows. We see this also in the NT, for example in Jesus' temptation in the desert: 'Then Jesus was by the Spirit Led to the desert to be tempted by the devil (Mat.4:1).
And Paul says in 2 Cor. 12:7, "To prevent me from exalting myself, I was (by God) a thorn in the flesh: I am tormented by a angel of Satan.'

Both also involve one event that can be viewed from two perspectives. 

2 Samuel described the event from God's perspective and 1 Chronicles from the power of sin and the punishment that follows, which is a recurring perspective in Chronicles.

The perspective of two authors may differ.