%I #25 Sep 08 2022 08:44:52
%S 1,4,8,16,20,32,32,36,48,56,64,60,64,88,84,96,88,104,108,120,128,116,
%T 144,136,140,168,160,168,164,176,192,180,208,200,216,228,200,240,220,
%U 264,248,236,264,264,288,284,264,296,292,312
%N Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n.
%H Amiram Eldar, <a href="/A036693/b036693.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F From _Reinhard Zumkeller_, Jan 13 2002: (Start)
%F a(n)/n ~ 2*Pi.
%F a(n) = A000328(n)-A000328(n-1). (End)
%e a(10^2) = 660, a(10^3) = 6392, a(10^4) = 62952, a(10^5) = 628520, a(10^6) = 6281404. - _Reinhard Zumkeller_, Jan 13 2002
%o (Magma)
%o [#[<x,y>: x in [-n..n], y in [-n..n]| n-1 lt r and r le n where r is Sqrt(x^2+ y^2)]: n in [0..50]]; // _Marius A. Burtea_, Feb 18 2020
%o (Sage)
%o def A036693(n):
%o if n == 0: return 1
%o Range = lambda n: ((i, j) for i in (-n..n) for j in (-n..n))
%o return sum(1 for (j, k) in Range(n) if (n-1)^2 < j^2 + k^2 <= n^2)
%o print([A036693(n) for n in range(20)]) # _Peter Luschny_, Mar 27 2020
%Y Cf. A000328.
%K nonn
%O 0,2
%A _Clark Kimberling_