A333462 - OEIS

%I #16 Mar 27 2020 13:49:21

%S 0,1,1,1,2,2,2,3,5,3,4,4,6,3,7,5,7,7,10,6,8,7,11,5,12,10,12,9,13,11,

%T 10,12,16,10,18,9,19,11,18,14,14,15,21,15,20,14,22,13,23,19,23,17,24,

%U 18,22,19,27,17,26,22,28,17,31,21,26,24,28,26,30,27,29,21

%N a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.

%H Hugo Pfoertner, <a href="/A333462/b333462.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) c=vectorsmall(2000000);for(x=1,1000,my(x2=x*x);c[x2]++;c[x2+x2]++;for(y=1,x-1,my(y2=y*y);c[x2+y2]+=2));

%o a(n)=sum(k=ceil((1+(n-1)^2)/4),floor(n^2/4),c[k]);

%o for(k=1,72,print1(a(k),", "))

%Y Cf. A004018, A232705, A333572, A333573.

%K nonn

%O 1,5

%A _Hugo Pfoertner_, Mar 26 2020