login
a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<=a.
5

%I #22 Oct 17 2019 16:42:10

%S 1,2,4,7,10,15,20,25,32,40,49,57,66,78,89,102,114,128,142,158,175,190,

%T 209,227,245,267,288,310,331,354,379,402,429,455,483,512,538,569,597,

%U 631,663,693,727,761,798,834,868,906,943,983

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

%C Row sums of the irregular triangle A255250. - _Wolfdieter Lang_, Mar 15 2015

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

%F a(n) - A036700(n) = 1+A049472(n). - _R. J. Mathar_, Oct 29 2011

%F 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 := proc(n)

%p local a,x,y ;

%p a := 0 ;

%p for x from 0 do

%p if x^2 > n^2 then

%p return a;

%p fi ;

%p for y from 0 to x do

%p if y^2+x^2 <= n^2 then

%p a := a+1 ;

%p end if;

%p end do;

%p end do:

%p end proc: # _R. J. Mathar_, Oct 29 2011

%t 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 a /@ Range[0, 49] (* _Jean-François Alcover_, Oct 17 2019 *)

%Y Cf. A036700, A049472, A000603, A000328, A255250.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_