%I #13 Aug 03 2018 16:03:00

%S 1,2,5,4,9,10,25,8,37,18,61,20,49,50,45,24,81,74,181,36,125,122,265,

%T 40,121,98,329,100,225,90,481,88,305,162,225,148,361,362,245,72,441,

%U 250,925,244,333,530,1105,120,1177,242,405,196,729,658,549,200,905,450,1741,180,961,962,925,344,441,610,2245

%N Number of squares in Z_n[i].

%C Equivalently, the number of distinct pairs (x^2-y^2, 2*x*y) mod n. - _Andrew Howroyd_, Aug 01 2018

%H Andrew Howroyd, <a href="/A271586/b271586.txt">Table of n, a(n) for n = 1..1000</a>

%e The squares in Z_3[i] are 0, i, 2i, 1 and 2, therefore a(3)=5.

%t GG[M_, s_] :=Table[Mod[(a + b I)^s, M], {a, M}, {b, M}] // Flatten // Union // Length; Table[GG[M, 2], {M, 1, 144}]

%o (PARI) a(n)={my(v=vector(n)); for(i=0, n-1, for(j=0, n-1, my(k=(i^2-j^2)%n + 1); v[k]=bitor(v[k], 1<<((2*i*j)%n)))); sum(j=1, n, hammingweight(v[j]))} \\ _Andrew Howroyd_, Aug 01 2018

%Y Cf. A000224.

%K nonn,mult

%O 1,2

%A _José María Grau Ribas_, Apr 10 2016

%E Keyword:mult added by _Andrew Howroyd_, Aug 01 2018