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A055410
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Number of points in Z^4 of norm <= n.
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9
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = [x^(n^2)] theta_3(x)^4/(1 - x), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 14 2018
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MATHEMATICA
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a[n_] := SeriesCoefficient[EllipticTheta[3, 0, x]^4/(1 - x), {x, 0, n^2}];
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PROG
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(C)
{
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;
(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])
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CROSSREFS
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Cf. A046895 (sizes of successive clusters in Z^4 lattice).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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