<p>One thing to note is that the Fibonacci heap is not really "based" on the Fibonacci number (its structure doesn't look at all like it's related to Fibonacci numbers); it's the <em>analysis</em> of the Fibonacci heap where the Fibonacci numbers appear.  You use the Fibonacci sequence to bound the number of trees in the heap of n elements with a value related to the nth Fibonacci number, thus demonstrating that the worst-case behavior of some of the operations can't be worse than O(log n).</p>

<p>As for your question about Pell numbers, I am not aware of any data structures that rely on the sequence (I actually hadn't encountered that sequence before!).  The Fibonacci sequence arises so much instead of other similar recurrent sequences due to a lot of interesting properties of the sequence that aren't necessarily true of other recurrence relations; I wrote about this <a href="https://stackoverflow.com/questions/4571670/what-is-it-about-fibonacci-numbers/4571782#4571782">in my answer to this question</a>.  I would assume that Pell numbers might be usable in some data structures or analyses, but the structure required to satisfy the recurrence relation doesn't seem to arise in any data structures or algorithms I have encountered.</p>

<p><strong>EDIT</strong>: I did find an interesting paper using Pell numbers in the analysis of certain sequences of values, which you can find <a href="http://arxiv.org/pdf/math/0205206v1" rel="nofollow noreferrer">here.</a></p>

<p>Hope this helps!</p>
Pell heap,just like Fibonacci heap
<p>Is there any heap based on Pell sequence(or Pell number) instead of Fibonacci number(like the Fibonacci heap)?</p>