A333462 a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.

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, 10, 12, 16, 10, 18, 9, 19, 11, 18, 14, 14, 15, 21, 15, 20, 14, 22, 13, 23, 19, 23, 17, 24, 18, 22, 19, 27, 17, 26, 22, 28, 17, 31, 21, 26, 24, 28, 26, 30, 27, 29, 21

Offset: 1

Author

Hugo Pfoertner, Mar 26 2020

Keywords

• nonn

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004018, A232705, A333572, A333573.

Programs

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));
a(n)=sum(k=ceil((1+(n-1)^2)/4),floor(n^2/4),c[k]);
for(k=1,72,print1(a(k),", "))