It does- I remember enough from Linear Algebra that vector spaces aren&#x27;t completely foreign, which helps a lot.<p>I think the generating-function method[1] is a case of pulling out a powertool (generating functions) to prove a simple thing to demonstrate the power of the tool, whereas your explanation takes the direct route and connects more of the threads about why it&#x27;s true.<p>[1] found an instance here: <a href="http:&#x2F;&#x2F;austinrochford.com&#x2F;posts&#x2F;2013-11-01-generating-functions-and-fibonacci-numbers.html" rel="nofollow">http:&#x2F;&#x2F;austinrochford.com&#x2F;posts&#x2F;2013-11-01-generating-functi...</a>