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 1-5 of 5 results.

A027843 Duplicate of A027840.

Original entry on oeis.org

1, 15, 220, 5275, 151086
Offset: 1

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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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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

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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

A027841 Number of subgroups of index n in fundamental group of a certain fiber space.

Original entry on oeis.org

1, 31, 301, 6491, 151711, 6673555, 362072313, 26375525171, 2384038557346, 264381564291841, 35133143655949285, 5515729547285229215, 1009373492449379396535, 212997911098253654157543, 51337590023914004777654131, 14016616814681248497416279139
Offset: 1

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Author

Keywords

Crossrefs

Formula

a(n) = Sum_{m|n} A027840(m) * (n/m)^(2*m+2). - Sean A. Irvine, Dec 07 2019

Extensions

More terms from Sean A. Irvine, Dec 07 2019

A027842 Number of subgroups of index n in fundamental group of a certain fiber space.

Original entry on oeis.org

1, 7, 34, 227, 1296, 10576, 77554, 729379, 7013419, 77371042, 910455096, 11877617828, 165087132666, 2480783846184, 39677415301224, 675818886754115, 12180498014887816, 231893906693650507, 4645789707491981892, 97740610362119850762, 2153888078209948673032
Offset: 1

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Author

Keywords

Crossrefs

Extensions

More terms from Sean A. Irvine, Dec 07 2019
Showing 1-5 of 5 results.