%N A1 Related to sum of two squares: Puzzle(?)

[Jeremy Gardiner]

On Wed, May 14, 2008 at 12:45 PM, zak seidov <zakseidov at yahoo.com> wrote:
> Here's result of my (interactive) session
> with Mathematica for A024352
> %N A024352 Numbers which are the difference of two
> squares
> %F Recurrency a[n]=a[n-1]+a[n-3]-a[n-4],a[1]==3,
> a[2]==5, a[3]==7, a[4]==8
> %F  a(n)= (1/9)*(15 + 15*n + 3*Cos[(2*n*Pi)/3] -
>      Sqrt[3]*Sin[(2*n*Pi)/3])}}
> %C First 200 terms
> {3,5,7,8,10,12,13,15,17,18,20,22,23,25,27,28,30,32,33,35,37,38,40,42,43,45,47,48,50,52,53,55,57,58,60,62,63,65,67,68,70,72,73,75,77,78,80,82,83,85,87,88,90,92,93,95,97,98,100,102,103,105,107,108,110,112,113,115,117,118,120,122,123,125,127,128,130,132,133,135,137,138,140,142,143,145,147,148,150,152,153,155,157,158,160,162,163,165,167,168,170,172,173,175,177,178,180,182,183,185,187,188,190,192,193,195,197,198,200,202,203,205,207,208,210,212,213,215,217,218,220,222,223,225,227,228,230,232,233,235,237,238,240,242,243,245,247,248,250,252,253,255,257,258,260,262,263,265,267,268,270,272,273,275,277,278,280,282,283,285,287,288,290,292,293,295,297,298,300,302,303,305,307,308,310,312,313,315,317,318,320,322,323,325,327,328,330,332,333,335}

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.

Regards,
Max