Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Here is an interesting problem:

The number of distince resistances that can be produced from n equal resistance resisters is given below.

The Sequence

Surprisingly this is also equal to the number of terms in nth order differentiation of a function y(x) with respect to x. How do I connect that these facts? That these represent the same counting and are expected to be equal.

P.S. I have only checked a few first terms of the differentiation. It may not be correct.

Edited. differentiation of a $nth$ power of function $y(x)$ with respect to $x$. E.G. $$\frac{dy^n}{dx}=ny^{n-1}y'$$

$$({y^n})''=n(n-1)y^{n-2}y'+ny^{n-1}y''$$ $$\vdots$$

ADDED Ok, if this sequence does not necessarily, explain this, how can I determine number of terms in this iteration? I found first five terms, if not mistaken to be $1, 2, 4, 9, 22, ...$

Added Serious! Error detected! Question is incorrect. Sorry!

share|improve this question
    
What kind of function y(x) are you referring to here, and how many terms have you checked? –  Foo Barrigno May 6 '13 at 12:57
    
up to 5 terms. I can't imagine taking 6th one. –  user45099 May 6 '13 at 13:06

1 Answer 1

up vote 2 down vote accepted

You say you've checked the first $5$ terms. Note that an OEIS search yields a full $36$ sequences containing these $5$ terms, many of which begin with those $5$ terms. You could be asking this question about any one of those sequences, with equal (lack of) justification. Unless you have a specific reason to believe that these two phenomena are related, there's nothing to explain here.

share|improve this answer
    
Sorry, that's what turned in google search. I didn't check other results. I will change question to different one. Thank you for the response. –  user45099 May 6 '13 at 13:18

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.