[seqfan] A000118: either as many, or thrice as many

[Pierre Abbat]

I squared A004018 as a power series (i.e. (1z⁰+4z¹+4z²+0z³+...)² = 
1z⁰+8z¹+24z²+32z³+...) and found that it's A000118, which is no surprise. 
a[n]=a[2n] when n is even (when squaring A004018, every other product is 0 
because one of the terms being multiplied is the (4m+3)rd term, which is 
always 0), and it appears that a[2n]=3a[n] when n is odd. How do you prove 
that, when n is odd, 2n has three times as many ways as n of being the sum of 
four squares? If I could prove this, I'd know for sure that A004018 is the 
coefficients of the power series of the khe function.

Pierre
-- 
When a barnacle settles down, its brain disintegrates.
Já não percebe nada, já não percebe nada.