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A036702 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<=a.

%I A036702 #22 Oct 17 2019 16:42:10
%S A036702 1,2,4,7,10,15,20,25,32,40,49,57,66,78,89,102,114,128,142,158,175,190,
%T A036702 209,227,245,267,288,310,331,354,379,402,429,455,483,512,538,569,597,
%U A036702 631,663,693,727,761,798,834,868,906,943,983
%N A036702 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<=a.
%C A036702 Row sums of the irregular triangle A255250. - _Wolfdieter Lang_, Mar 15 2015
%H A036702 <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>
%F A036702 a(n) - A036700(n) = 1+A049472(n). - _R. J. Mathar_, Oct 29 2011
%F A036702 a(n) = sum(floor(sqrt(n^2 - m^2)) - (m-1), m = 0.. floor(n/sqrt(2))), n >= 0. See A255250.  - _Wolfdieter Lang_, Mar 15 2015
%p A036702 A036702 := proc(n)
%p A036702         local a,x,y ;
%p A036702         a := 0 ;
%p A036702         for x from 0 do
%p A036702                 if x^2 > n^2 then
%p A036702                         return a;
%p A036702                 fi ;
%p A036702                 for y from 0 to x do
%p A036702                         if y^2+x^2 <= n^2 then
%p A036702                                 a := a+1 ;
%p A036702                         end if;
%p A036702                 end do;
%p A036702         end do:
%p A036702 end proc: # _R. J. Mathar_, Oct 29 2011
%t A036702 a[n_] := Module[{a, b}, If[n == 0, 1, Reduce[a^2 + b^2 <= n^2 && a >= 0 && 0 <= b <= a, {a, b}, Integers] // Length]];
%t A036702 a /@ Range[0, 49] (* _Jean-François Alcover_, Oct 17 2019 *)
%Y A036702 Cf. A036700, A049472, A000603, A000328, A255250.
%K A036702 nonn,easy
%O A036702 0,2
%A A036702 _Clark Kimberling_