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A036702 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>=0, 0<=b<=a. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..49.

Index entries for Gaussian integers and primes

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

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-Fran├žois Alcover, Oct 17 2019 *)

CROSSREFS

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

Sequence in context: A095116 A027384 A022939 * A007983 A049640 A179385

Adjacent sequences:  A036699 A036700 A036701 * A036703 A036704 A036705

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)