A036698 - OEIS

A036698

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

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

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OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for Gaussian integers and primes

FORMULA

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

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

a(n) = A014200(n^2). - Seiichi Manyama, Dec 20 2021

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

(PARI) a(n) = sum(k=1, n^2, sumdiv(k, d, kronecker(-4, k/d))); \\ Seiichi Manyama, Dec 20 2021

CROSSREFS

Cf. A000603, A014200.

Sequence in context: A172115 A328655 A091369 * A279169 A374352 A132273

Adjacent sequences: A036695 A036696 A036697 * A036699 A036700 A036701

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved