Could any (or all) of Mathematica, Maxima, Axiom derive and verify/validate recurrence formula derived from gf ?

[Maximilian Hasler]

> That's strange. Why 4 = 2^2 - 0^2 and 9 = 5^2 - 4^2 are missed here?
> Anyway, the current description and recurrence are too complicated.
>
> In general, an integer is the difference of two squares as soon as it
> is not 2 modulo 4. And this sequence is A042965.

obviously the "guessed" (what code?) g.f. is wrong, but no need to
worry, on OEIS all is OK:

%S A024352 3,5,7,8,9,11,12,13,15,16,17,19,20,21,23,24,25,27,28,29,31,32,33,35,
%N A024352 Numbers which are the difference of two squares.
%Y A024352 Same as A042965 except for initial terms - Michael Somos,
Jun 08, 2000.