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A036698 a(n)=number of Gaussian integers z=a+bi satisfying |z|<=n, a>0, b>=0. 1
0, 1, 3, 7, 12, 20, 28, 37, 49, 63, 79, 94, 110, 132, 153, 177, 199, 225, 252, 282, 314, 343, 379, 413, 448, 490, 530, 572, 613, 657, 705, 750, 802, 852, 906, 963, 1013, 1073, 1128, 1194, 1256, 1315, 1381, 1447, 1519, 1590, 1656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..46.

Index entries for Gaussian integers and primes

FORMULA

a(n) = n^2 * Pi/4 + O(n). - Charles R Greathouse IV, Apr 03 2013

PROG

(C)

typedef unsigned long ulong;

ulong A036698(ulong i)

{

    const ulong ring = i*i;

    ulong result = 0;

    for(ulong a = 1; a <= i; a++)

    {

        const ulong a2 = a*a;

        for(ulong b = 0; b <= i; b++)

        {

            ulong z = a2 + b*b;

            if ( ring >= z ) result++;

        }

    }

    return result;

} /* Oskar Wieland, Apr 02 2013 */

(PARI) a(n)=my(n2=n^2); sum(a=1, n, sqrtint(n2-a^2)+1) \\ Charles R Greathouse IV, Apr 03 2013

CROSSREFS

a(n) = A000603(n) - n - 1.

Sequence in context: A002498 A172115 A091369 * A279169 A132273 A130050

Adjacent sequences:  A036695 A036696 A036697 * A036699 A036700 A036701

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 20 10:23 EST 2018. Contains 297960 sequences.