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A036700 Number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b

%I A036700 #17 Nov 23 2020 01:43:41
%S A036700 0,1,2,4,7,11,15,20,26,33,41,49,57,68,79,91,102,115,129,144,160,175,
%T A036700 193,210,228,249,269,290,311,333,357,380,406,431,458,487,512,542,570,
%U A036700 603,634,664,697,730,766,802,835,872,909,948,988
%N A036700 Number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<a.
%H A036700 Wikipedia, <a href="http://en.wikipedia.org/wiki/Gaussian_integers">Gaussian Integers</a>
%H A036700 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F A036700 Partial sums of A036701. - _Sean A. Irvine_, Nov 22 2020
%p A036700 A036700 := proc(n)
%p A036700         local a,x,y ;
%p A036700         a := 0 ;
%p A036700         for x from 0 do
%p A036700                 if x^2 > n^2 then
%p A036700                         return a;
%p A036700                 fi ;
%p A036700                 for y from 0 to x-1 do
%p A036700                         if y^2+x^2 <= n^2 then
%p A036700                                 a := a+1 ;
%p A036700                         end if;
%p A036700                 end do;
%p A036700         end do:
%p A036700 end proc: # _R. J. Mathar_, Oct 29 2011
%Y A036700 Cf. A036701, A036702.
%K A036700 nonn
%O A036700 0,3
%A A036700 _Clark Kimberling_