generating function for interesting sequence

[Franklin T. Adams-Watters]

"Andrew Plewe" <aplewe at sbcglobal.net> wrote:
>I've stumbled on an interesting sequence (although for some reason it looks
>familiar...) and I'm looking for a generating function a(n).  First, a few
>terms of the sequence:
>
>Which is a triangle read by anti-diagonals:
>
>3   8   15  24  35  48
>5   12  21  32  45
>7   16  27  40
>9   20  33
>11  24
>13

Well, first of all, there clearly should be another line before this:
1   4    9  16  25  36  49
3   8   15  24  35  48
5   12  21  32  45
7   16  27  40
9   20  33
11  24
13

And we can see that the sequence is differences of two squares:
  1-0   4-0   9-0  16-0  25-0  36-0  49-0
  4-1   9-1  16-1  25-1  36-1  49-1
  9-4  16-4  25-4  36-4  49-4
 16-9  25-9  36-9  49-9
 25-16 36-16 49-16
 36-25 49-25
 49-36
>    -Andrew Plewe-

-- 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645


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