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 1-4 of 4 results.

A268572 Number of bicolored immersions of unoriented circle into oriented sphere with n double points and no simple loop.

Original entry on oeis.org

0, 0, 2, 1, 4, 9, 38, 133, 640, 2864
Offset: 1

Views

Author

N. J. A. Sloane, Mar 03 2016

Keywords

Crossrefs

Formula

a(2*n) = A268568(2*n), a(2*n+1) = 2 * A268569(2*n+1). - Andrey Zabolotskiy, Jun 05 2024

Extensions

Name clarified by Andrey Zabolotskiy, Jun 08 2024

A268559 Number of bicolored immersions of unoriented circle into oriented surface with n double points, up to stable geotopy.

Original entry on oeis.org

2, 3, 14, 54, 420, 3886, 46470, 645524, 10328214
Offset: 1

Views

Author

N. J. A. Sloane, Mar 02 2016

Keywords

Crossrefs

Extensions

Name clarified by Andrey Zabolotskiy, Jun 09 2024

A268573 Number of irreducible indecomposable bicolored immersions of unoriented circle into oriented sphere with n double points.

Original entry on oeis.org

0, 0, 2, 1, 4, 6, 24, 73, 322, 1274
Offset: 1

Views

Author

N. J. A. Sloane, Mar 03 2016

Keywords

Crossrefs

Formula

a(2*n) = A264761(2*n), a(2*n+1) = 2 * A264760(2*n+1). - Andrey Zabolotskiy, Jun 05 2024

Extensions

Name clarified by Andrey Zabolotskiy, Jun 08 2024

A268560 Number of bicolored maps defined by immersions of unoriented circle into oriented sphere with n double points with edges labeled 1..2*n such that labels of successive edges along the curve (starting at any edge, going in the direction determined by the coloring) are encountered in pairs of the form {2*m-1, 2*m} (in either order).

Original entry on oeis.org

2, 16, 336, 12480, 689664, 51440640, 4870932480, 561752432640, 76597275525120, 12077498082263040, 2164587437201817600, 434984457687426662400, 96927605985557820211200, 23730144990202925206732800, 6333914501366616792288460800, 1831049666989439061980086272000
Offset: 1

Views

Author

N. J. A. Sloane, Mar 02 2016

Keywords

Crossrefs

Formula

a(n) = A268567(n) * 2^n [proof: labeling the vertex incident to a pair {2*m-1, 2*m} by m defines a 2^n-to-one map from edge-labeled curves to vertex-labeled curves; and a bijection between vertex-labeled bicolored unoriented immersions and vertex-labeled (uncolored) oriented immersions can be defined e.g. by requiring that the pair of edges going from vertex #1 is incident to a shaded region]. - Andrey Zabolotskiy, Jan 14 2025

Extensions

New name and terms a(11) onwards from Andrey Zabolotskiy, Jan 21 2025
Showing 1-4 of 4 results.