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 1-3 of 3 results.

A027840 Number of subgroups of index n in fundamental group of a certain fiber space.

Original entry on oeis.org

1, 15, 220, 5275, 151086, 6605004, 362069912, 26370058035, 2384037107365, 264380945199210, 35133143655934644, 5515729438742221708, 1009373492449379367974, 212997911074525038601560, 51337590023913924398371080, 14016616814674335739387516003
Offset: 1

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Crossrefs

Extensions

Third term corrected from 240 to 220, Aug 15 1999
More terms from Sean A. Irvine, Dec 07 2019

A027838 Number of subgroups of index n in fundamental group of a certain fiber space.

Original entry on oeis.org

1, 7, 22, 111, 486, 3772, 29142, 275871, 2830459, 32028882, 392744078, 5201524044, 73943424582, 1123603726896, 18176728661832, 311951284854975, 5661698774848910, 108355867352001811, 2181096921557783966, 46066653293892718506, 1018705098450761473704
Offset: 1

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Author

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References

  • V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
  • R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), Eq. (5.125).

Crossrefs

Formula

a(n) = Sum_{m|n} A003319(m+1) * (n/m)^(m+1). - Sean A. Irvine, Dec 06 2019

Extensions

More terms from Sean A. Irvine, Dec 06 2019

A027839 Number of subgroups of index n in fundamental group of a certain fiber space.

Original entry on oeis.org

1, 15, 124, 2431, 68766, 3025596, 173773496, 12786773247, 1169623901221, 130305653188890, 17376934722757908, 2733655198336260124, 501034099176714376118, 105847486572700895182728, 25534322201330399433420024, 6976464857439636995547805183
Offset: 1

Views

Author

Keywords

References

  • V. A. Liskovets and A. Mednykh, Enumeration of subgroups in the fundamental groups of orientable circle bundles over surfaces, Commun. in Algebra, 28, No. 4 (2000), 1717-1738.
  • R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.13(c), Eq. (5.125).

Crossrefs

Formula

a(n) = Sum_{m|n} A027837(m) * (n/m)^(2*m+1). - Sean A. Irvine, Dec 06 2019

Extensions

More terms from Sean A. Irvine, Dec 06 2019
Showing 1-3 of 3 results.