Numbers with "perfect" figurate representation

[Max Alekseyev]

On Sun, Mar 30, 2008 at 10:59 PM, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> I'm re-evaluating the sequence you
> came up with; so far I've verified these values up to and including 30:
>
>  6,9,25,30

Why 9 is here?

Except for that number, this sequence seems to be the numbers of the
form a*(2*r+1) where r^2 < a <= r*(r+1).

r=1: a=2  ~ 6
r=2: a=5  ~ 25
r=2: a=6  ~ 30
r=3: a=10 ~ 70
r=3: a=11 ~ 77
r=3: a=12 ~ 84
...

Regards,
Max