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

0, 1, 2, 4, 7, 11, 15, 20, 26, 33, 41, 49, 57, 68, 79, 91, 102, 115, 129, 144, 160, 175, 193, 210, 228, 249, 269, 290, 311, 333, 357, 380, 406, 431, 458, 487, 512, 542, 570, 603, 634, 664, 697, 730, 766, 802, 835, 872, 909, 948, 988

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• Wikipedia, Gaussian Integers
• Index entries for Gaussian integers and primes

Crossrefs

Cf. A036701, A036702.

Programs

Maple

A036700 := 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-1 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

Formula

Partial sums of A036701. - Sean A. Irvine, Nov 22 2020