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 A055410 Number of points in Z^4 of norm <= n. 9
 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 Andrew Howroyd, Table of n, a(n) for n = 0..500 FORMULA a(n) = A046895(n^2). - Joerg Arndt, Apr 08 2013 a(n) = [x^(n^2)] theta_3(x)^4/(1 - x), where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 14 2018 MATHEMATICA a[n_] := SeriesCoefficient[EllipticTheta[3, 0, x]^4/(1 - x), {x, 0, n^2}]; a /@ Range[0, 30] (* Jean-François Alcover, Sep 23 2019, after Ilya Gutkovskiy *) 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 Column k=4 of A302997. Cf. A046895 (sizes of successive clusters in Z^4 lattice). Sequence in context: A178369 A328492 A306686 * A214616 A175371 A291893 Adjacent sequences:  A055407 A055408 A055409 * A055411 A055412 A055413 KEYWORD nonn AUTHOR STATUS approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)