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%I #30 Sep 23 2019 09:58:24
%S 1,9,89,425,1281,3121,6577,11833,20185,32633,49689,72465,102353,
%T 140945,190121,250553,323721,411913,519025,643441,789905,961721,
%U 1156217,1380729,1638241,1927297,2257281,2624417,3035033,3490601,4000425
%N Number of points in Z^4 of norm <= n.
%H Andrew Howroyd, <a href="/A055410/b055410.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = A046895(n^2). - _Joerg Arndt_, Apr 08 2013
%F a(n) = [x^(n^2)] theta_3(x)^4/(1 - x), where theta_3() is the Jacobi theta function. - _Ilya Gutkovskiy_, Apr 14 2018
%t a[n_] := SeriesCoefficient[EllipticTheta[3, 0, x]^4/(1 - x), {x, 0, n^2}];
%t a /@ Range[0, 30] (* _Jean-François Alcover_, Sep 23 2019, after _Ilya Gutkovskiy_ *)
%o (C)
%o int A055410(int i)
%o {
%o const int ring = i*i;
%o int result = 0;
%o for(int a = -i; a <= i; a++)
%o for(int b = -i; b <= i; b++)
%o for(int c = -i; c <= i; c++)
%o for(int d = -i; d <= i; d++)
%o if ( ring >= a*a + b*b + c*c + d*d ) result++;
%o return result;
%o } /* _Oskar Wieland_, Apr 08 2013 */
%o (PARI)
%o N=66; q='q+O('q^(N^2));
%o t=Vec((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^4/(1-q)); /* A046895 */
%o vector(sqrtint(#t),n,t[(n-1)^2+1])
%o /* _Joerg Arndt_, Apr 08 2013 */
%Y Column k=4 of A302997.
%Y Cf. A046895 (sizes of successive clusters in Z^4 lattice).
%K nonn
%O 0,2
%A _David W. Wilson_
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