##Python 2, 55 bytes

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    def f(x,n):l=[1]*n;exec"print l[0];l=l[1:]+[sum(l)];"*x

Tracks a length-`n` window of the sequence in the list `l`, updated by appending the sum and removing the first element. Prints the first element each iteration for `x` iterations.

A different approach of storing all the elements and summing the last `n` values gave the same length (55).

    def f(x,n):l=[1]*n;exec"l+=sum(l[-n:]),;"*x;print l[:x]