[seqfan] Re: A000041 partition sequence

[William Keith]

Bob:

     I'm afraid I don't understand what you're trying to do.  Several of
your statements don't make sense to me.  For instance, "1 + F(G) solves for
a(n)"?  One typically solves equations, and this is not an equation.  Is
this some way of recovering the sequence of partition numbers after a
series of operations on itself?

     Could you give some explicit examples of the calculations you are
describing?

     It is known that any partition number p(n) can be written as

p(n) =  p(n-1) + p(n-2) - p(n-5) - p(n-7) + p(n-12) + p(n-15) - ...

where the numbers being subtracted are known as the pentagonal numbers, and
eventually the terms become zero.  Perhaps this is related to the ideas you
are having.

William Keith