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%I #21 Nov 14 2019 05:29:46
%S 1,8,12,16,32,28,40,40,48,68,56,72,68,88,88,84,112,112,112,116,112,
%T 144,140,144,144,168,164,160,184,172,200,192,188,208,224,224,228,224,
%U 248,236,264,248,264,276,264,288,276,304,304,312
%N Number of Gaussian integers z=a+bi satisfying n - 1/2 < |z| <= n + 1/2.
%C 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
%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%t 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}]];
%t a /@ Range[0, 49] (* _Jean-François Alcover_, Nov 14 2019 *)
%o (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
%Y Cf. A047077, A232705.
%K nonn
%O 0,2
%A _Clark Kimberling_
%E Edited by _Ralf Stephan_, Nov 28 2013
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