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A055410 Number of points in Z^4 of norm <= n. 4
1, 9, 89, 425, 1281, 3121, 6577, 11833, 20185, 32633, 49689, 72465, 102353, 140945, 190121, 250553, 323721, 411913, 519025, 643441, 789905, 961721, 1156217, 1380729, 1638241, 1927297, 2257281, 2624417, 3035033, 3490601, 4000425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

FORMULA

a(n) = A046895(n^2). [Joerg Arndt, Apr 08 2013]

PROG

(C)

int A055410(int i)

{

    const int ring = i*i;

    int result = 0;

    for(int a = -i; a <= i; a++)

        for(int b = -i; b <= i; b++)

            for(int c = -i; c <= i; c++)

                for(int d = -i; d <= i; d++)

                    if ( ring >= a*a + b*b + c*c + d*d ) result++;

    return result;

} /* Oskar Wieland, Apr 08 2013 */

(PARI)

N=66;  q='q+O('q^(N^2));

t=Vec((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^4/(1-q)); /* A046895 */

vector(sqrtint(#t), n, t[(n-1)^2+1])

/* Joerg Arndt, Apr 08 2013 */

CROSSREFS

Cf. A046895 (sizes of successive clusters in Z^4 lattice).

Sequence in context: A279166 A147884 A178369 * A214616 A175371 A217321

Adjacent sequences:  A055407 A055408 A055409 * A055411 A055412 A055413

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified May 25 14:13 EDT 2017. Contains 287038 sequences.