[seqfan] Re: Currency puzzle

[Rob Pratt]

Alternatively, the first GF accounts for unordered partitions in which a coin and a bill of the same value cannot both appear.  For value k, neither coin nor bill appears, coin appears only, or bill appears only, yielding x^0 + x^k + x^k = 1 + 2x^k.  Equivalently, (1 + x^k)^2 - (x^k)^2 = 1 + 2x^k.

> On Sep 27, 2015, at 4:11 AM, Joerg Arndt <arndt at jjj.de> wrote:
> 
> 
> About 
>> G.F.: (1+x)(1+2x^2)(1+x^3)(1+2x^4)(1+2x^8)(1+2x^16)(1+2x^32)(1+2x^64)
> versus
>  G.F.: (1+x)(1+x^2)^2(1+x^3)(1+x^4)^2(1+x^8)^2(1+x^16)^2(1+x^32)^2(1+x^64)^2
> 
> The first accounts for ordered sorts, the second for un-ordered
> which is more common with partitions.  "Ordered" is more common
> with compositions ("ordered partitions").
> 
> Regards,  jj
> 
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