4 Fix tex

Let's say we have a sequence T(n) $T(n)$ with the corresponding generating function

A(t)

$$A(t) = \sum \sb {n sum_{n = 0} ^ \infty 0}^\infty T(n) t^n (sorry it won't let me save an edit with image with it) t^n$$

Is there some relationship between the two functions A(t) $A(t)$ and A(t^2)? $A(t^2)$? And for that matter is there some generalization for any integer power or t?

edit--$t$?

Edit: I'm actually trying to solve for the generating function A(t) $A(t)$ in the equation

A(t)

$$A(t) + (1+t)A(t^2) = t/(1-t^2)t/(1-t^2)$$

this is what inspired my question. My intuition suggested to me that I should look for some kind of relationship between A(t^2) $A(t^2)$ and A(t), $A(t)$, hence the vagueness of my question.

3 added 241 characters in body

Let's say we have a sequence T(n) with the corresponding generating function

A(t) = \sum \sb {n = 0} ^ \infty T(n) t^n

(sorry it won't let me save an edit with image with it)

Is there some relationship between the two functions A(t) and A(t^2)? And for that matter is there some generalization for any integer power or t?

edit--

I'm actually trying to solve for the generating function A(t) in the equation

A(t) + (1+t)A(t^2) = t/(1-t^2)

this is what inspired my question. My intuition suggested to me that I should look for some kind of relationship between A(t^2) and A(t), hence the vagueness of my question.

2 added 64 characters in body; deleted 6 characters in body

Lets

Let's say we have a sequence T(n) with the corresponding generating function

A(t) = \sum _ {n = 0} ^ \infty T(n) t^n

is

Is there some relationship between the two functions A(t) and A(t^2) A(t^2)? And for that matter is there some generalization for any integer power or t?

(sorry I can't render these because I am a new user.)

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