cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A373881 Number of lattice points inside the ball x^2 + y^2 + z^2 <= 10^n.

Original entry on oeis.org

7, 147, 4169, 132451, 4187857, 132459677, 4188781437, 132461190717, 4188790061109, 132461176423805, 4188790203273025, 132461176878317635
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2024

Keywords

Crossrefs

Cf. A068785, A373882, A373883, A373884, A373885, A373896.
Cf. A000605, A117609.

Programs

  • 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

A373883 Number of lattice points inside or on the 5-dimensional hypersphere x_1^2 + x_2^2 + x_3^2 + x_4^2 + x_5^2 = 10^n.

Original entry on oeis.org

11, 1903, 532509, 166711479, 52646439609, 16645828150193, 5263797438037625, 1664556518763850069, 526378909839312477785, 166455624316184206850205, 52637890147973140623040513, 16645562406807092052281075983, 5263789013922669372094091725857
Offset: 0

Views

Author

Seiichi Manyama, Jun 21 2024

Keywords

Crossrefs

Cf. A068785, A373881, A373882, A373884, A373885, A373896.
Cf. A055411, A175360.

Programs

  • 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(5, 10^n);

Formula

a(n) = A175360(10^n).

Extensions

a(7) from Chai Wah Wu, Jun 22 2024
a(8)-a(10) from Chai Wah Wu, Jun 23 2024
a(11)-a(12) from Chai Wah Wu, Jun 24 2024
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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