Question is not very clear about the context of word 'sequence' here.
If I am to select 4 numbers out of four and arrange them in order then there are 4!*8C4 = 1680 different sequences possible.
If the word sequence refers to some arithmetic sequence or geometric sequence, then counting is going to change for sure.
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There are infinitely many possible number sequences, and infinitely many numbers which can appear in those sequences. Any and every number can appear in a number sequence.
Three numbers can be arranged in 27 different sequences if repetition is allowed, and in 6 different sequences if it's not.
There are infinitely many possible answers. One possible quartet is (1,1,1,235)
625 if numbers can have leading 0s, 500 otherwise.
There are many possible quartets: for example, 1,1,2 and 25.