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

1, 2, 4, 7, 10, 15, 20, 25, 32, 40, 49, 57, 66, 78, 89, 102, 114, 128, 142, 158, 175, 190, 209, 227, 245, 267, 288, 310, 331, 354, 379, 402, 429, 455, 483, 512, 538, 569, 597, 631, 663, 693, 727, 761, 798, 834, 868, 906, 943, 983

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Row sums of the irregular triangle A255250. - Wolfdieter Lang, Mar 15 2015

Links

• Index entries for Gaussian integers and primes

Crossrefs

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

Programs

Maple

A036702 := proc(n)
        local a,x,y ;
        a := 0 ;
        for x from 0 do
                if x^2 > n^2 then
                        return a;
                fi ;
                for y from 0 to x do
                        if y^2+x^2 <= n^2 then
                                a := a+1 ;
                        end if;
                end do;
        end do:
end proc: # R. J. Mathar, Oct 29 2011

Mathematica

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]];
a /@ Range[0, 49] (* Jean-François Alcover, Oct 17 2019 *)

Formula

a(n) - A036700(n) = 1+A049472(n). - R. J. Mathar, Oct 29 2011

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