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

0,1

Links

Table of n, a(n) for n=0..11.

Formula

a(n) = A117609(10^n).

Limit_{n->oo) a(n) = (4*Pi/3)*(10^n)^(3/2). - Hugo Pfoertner, Jun 21 2024

Prog

(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);

Crossrefs

Cf. A068785, A373882, A373883, A373884, A373885, A373896.

Cf. A000605, A117609.

Sequence in context: A342113 A211108 A251668 * A376227 A048935 A291677

Adjacent sequences: A373878 A373879 A373880 * A373882 A373883 A373884

Keyword

nonn,more

Author

Seiichi Manyama, Jun 21 2024

Extensions

a(7)-a(10) from Hugo Pfoertner, Jun 21 2024

a(11) from Chai Wah Wu, Jun 24 2024

Status

approved