req proof regarding A196

[Mitch Harris]

Joseph Biberstine wrote:

>I suppose it is illuminative that A33638 are numbers of the form n^2+1
>or n^2+n+1 (credit Donald S. McDonald), though I'm not quite bright
>enough to see how.

The "+1" is a red herring.

Consider just the quarter squares floor(n^2/4) (A002620) which is also 
floor(n/2)ceil(n/2).

If even you get
   f(2n) = n^2,
if odd you get
   f(2n+1) = n^2+n = n(n+1)

So not only does it have numbers both of those two forms but they also 
interleave.

The complicated description was the combinatorial construction by the 
original sequence author which led to the sequence (similar to the Ulam 
description).

Mitch