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.

A373694 Number of incongruent n-sided periodic Reinhardt polygons.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 5, 0, 1, 5, 1, 2, 10, 1, 1, 12, 4, 1, 23, 2, 1, 38, 1, 0, 64, 1, 12, 102, 1, 1, 191, 12, 1, 329, 1, 2, 633, 1, 1, 1088, 9, 34, 2057, 2, 1, 3771, 66, 12, 7156, 1, 1, 13464, 1, 1, 25503, 0, 193, 48179, 1, 2, 92206, 358, 1, 175792, 1, 1, 338202
Offset: 1

Views

Author

Bernd Mulansky, Aug 04 2024

Keywords

Crossrefs

Programs

  • Mathematica
    dD[m_] := 2^Floor[(m - 3)/2] + Sum[2^(m/d) EulerPhi[d], {d, DeleteCases[Divisors[m], _?EvenQ]}]/4/m;
    a[n_] := Sum[dD[n/d] MoebiusMu[2 d], {d, DeleteCases[Divisors[n], 1]}];

Formula

a(n) = A374832(n) - A373695(n).
a(n) = Sum_{d|n, d>1} D(n/d)*Mu(2d), with D(m) = 2^floor((m-3)/2) + (Sum_{d|m, d odd} 2^(m/d)*Phi(d) )/(4m), where Mu is MoebiusMu and Phi is EulerPhi.

A374832 Number of incongruent n-sided Reinhardt polygons.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 5, 0, 1, 5, 1, 2, 10, 1, 1, 12, 4, 1, 23, 2, 1, 41, 1, 0, 64, 1, 12, 102, 1, 1, 191, 12, 1, 338, 1, 2, 777, 1, 1, 1088, 9, 34, 2057, 2, 1, 3771, 66, 12, 7156, 1, 1, 17856, 1, 1, 26811, 0, 193, 48272, 1, 2, 92206, 385, 1, 175792
Offset: 1

Views

Author

Bernd Mulansky, Jul 21 2024

Keywords

References

  • Karl Reinhardt, Extremale Polygone gegebenen Durchmessers. Jahresber. Deutsche Math.-Verein. 31 (1922): 251-70.

Crossrefs

Formula

a(n) = A373694(n) + A373695(n). - Bernd Mulansky, Aug 23 2024

Extensions

More terms from Bernd Mulansky, Aug 23 2024
Showing 1-2 of 2 results.