A036705 Number of Gaussian integers z=a+bi satisfying n - 1/2 < |z| <= n + 1/2.

1, 8, 12, 16, 32, 28, 40, 40, 48, 68, 56, 72, 68, 88, 88, 84, 112, 112, 112, 116, 112, 144, 140, 144, 144, 168, 164, 160, 184, 172, 200, 192, 188, 208, 224, 224, 228, 224, 248, 236, 264, 248, 264, 276, 264, 288, 276, 304, 304, 312

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

Number of integer Cartesian grid points covered by a ring around the origin with width 1 and outer radius n + 1/2. - Ralf Stephan, Nov 28 2013

Links

• Index entries for Gaussian integers and primes

Crossrefs

Cf. A047077, A232705.

Programs

Mathematica

a[n_] := If[n==0, 1, inf = (n-1/2)^2; sup = (n+1/2)^2; 4 Sum[Boole[inf < x^2 + y^2 < sup], {x, 0, n}, {y, 1, n}]];
a /@ Range[0, 49] (* Jean-François Alcover, Nov 14 2019 *)

PARI

a(n)=sum(i=-n, n, sum(j=-n, n, d=sqrt(i*i+j*j); if(d>=n-1/2&&d<=n+1/2, 1))) \\ Ralf Stephan, Nov 28 2013

Extensions

Edited by Ralf Stephan, Nov 28 2013