A255250 -id:A255250 - cp's OEIS frontend

A256094 Alternating row sums of array A255250.

1, 2, 2, 3, 4, 3, 4, 5, 4, 6, 7, 7, 8, 8, 7, 8, 8, 10, 10, 12, 13, 14, 11, 13, 13, 11, 14, 16, 15, 18, 17, 16, 15, 17, 17, 20, 20, 23, 23, 21, 21, 21, 19, 23, 22, 24, 26, 26, 23, 25, 24, 28, 29, 31, 30, 32, 29, 31, 28, 29, 31

Offset: 0

Wolfdieter Lang, Mar 14 2015

See A255250 for a comment on Gauss's circle problem in an octant and a link.

Cf. A255250.

a(n) = sum((-1)^m*T(n, m), m=0..floor(n/sqrt(2))), n >= 0, with T(n, m) = A255250(n, m) = floor(sqrt(n^2 - m^2)) - (m-1).

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

Original entry on oeis.org

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

Clark Kimberling

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

Index entries for Gaussian integers and primes

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

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

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 *)

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

cp's OEIS Frontend

A256094 Alternating row sums of array A255250.

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

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