Sum Over Coprime Elements: Inversion Formula

[Christian G.Bower]

------ Original Message ------
From: franktaw at netscape.net
To: seqfan at ext.jussieu.fr
Subject: Re: Sum Over Coprime Elements: Inversion Formula

> Interesting.
>  
> It appears that the diagonals are all periodic.  (Just observation, looking
at 40 rows; I haven't tried to prove any of this.)
> Period 1: [1]
> Period 2: [-1,0]
> Period 3: [-1,-1,0]
> Period 6: [1,0,0,0,0,0]
> Period 15: [-1,0,-1,-1,1,-1,-1,0,-1,0,0,-1,-1,0,0]
> Period 30: [1,0,2,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,2,0,1,0,0,0,2,0,0,0]
> Period ???:
[1,0,0,1,0,0,2,-1,0,0,0,0,0,1,-1,1,0,0,1,0,1,1,-1,0,0,0,0,1,0,-1,1,0,0,1,...]
>  
> The sequence 1,2,3,6,15,30 is not in the OEIS.  To this point, each term
a(n)=n*a(n-1)/b(n-1), where b(n) is 1,2,2,2,3.
>  
> Franklin T. Adams-Watters

The next terms of a appear to be 105,210,105,210,(>489) making the next terms
of b: 2,4,18,5

Christian