A036695 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, b>=0.

1, 4, 9, 18, 29, 46, 63, 82, 107, 136, 169, 200, 233, 278, 321, 370, 415, 468, 523, 584, 649, 708, 781, 850, 921, 1006, 1087, 1172, 1255, 1344, 1441, 1532, 1637, 1738, 1847, 1962, 2063, 2184, 2295, 2428, 2553, 2672, 2805, 2938

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for Gaussian integers and primes

Crossrefs

Cf. A000603, A000328, A036696.

Programs

Haskell

a036695 n = length [(x,y) | x <- [-n..n], y <- [0..n], x^2 + y^2 <= n^2]
-- Reinhard Zumkeller, Jan 23 2012

Mathematica

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 *)

Formula

Partial sums of A036696. - Sean A. Irvine, Nov 22 2020