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a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, b>=0.
3

%I #24 Nov 23 2020 01:43:31

%S 1,4,9,18,29,46,63,82,107,136,169,200,233,278,321,370,415,468,523,584,

%T 649,708,781,850,921,1006,1087,1172,1255,1344,1441,1532,1637,1738,

%U 1847,1962,2063,2184,2295,2428,2553,2672,2805,2938

%N a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, b>=0.

%C Number of ordered pairs of integers (x,y) with x^2 + y^2 <= n^2 and y >= 0. [_Reinhard Zumkeller_, Jan 23 2012]

%H Reinhard Zumkeller, <a href="/A036695/b036695.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>

%F Partial sums of A036696. - _Sean A. Irvine_, Nov 22 2020

%t a[n_] := (k = 0; Do[If[x^2 + y^2 <= n^2, k++], {x, -n, n}, {y, 0, n}]; k); Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Oct 08 2016 *)

%o (Haskell)

%o a036695 n = length [(x,y) | x <- [-n..n], y <- [0..n], x^2 + y^2 <= n^2]

%o -- _Reinhard Zumkeller_, Jan 23 2012

%Y Cf. A000603, A000328, A036696.

%K nonn

%O 0,2

%A _Clark Kimberling_