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A036693 Number of Gaussian integers z = a + bi satisfying n-1 < |z| <= n. 2

%I

%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_

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Last modified May 16 12:46 EDT 2021. Contains 343947 sequences. (Running on oeis4.)