A373881 Number of lattice points inside the ball x^2 + y^2 + z^2 <= 10^n.
7, 147, 4169, 132451, 4187857, 132459677, 4188781437, 132461190717, 4188790061109, 132461176423805, 4188790203273025, 132461176878317635
Offset: 0
Programs
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PARI
b(k, n) = my(q='q+O('q^(n+1))); polcoef((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^k/(1-q), n); a(n) = b(3, 10^n);
Formula
a(n) = A117609(10^n).
Limit_{n->oo} a(n) = (4*Pi/3)*(10^n)^(3/2). - Hugo Pfoertner, Jun 21 2024
Extensions
a(7)-a(10) from Hugo Pfoertner, Jun 21 2024
a(11) from Chai Wah Wu, Jun 24 2024