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.

A288033 Number of (undirected) paths in the n X n king graph.

Original entry on oeis.org

0, 30, 5148, 6014812, 57533191444, 4956907379126694, 3954100866385811897908, 29986588563791584765930866780, 2187482261973324160097873804506155572, 1550696105068168200375810546149511240714556526
Offset: 1

Views

Author

Eric W. Weisstein, Jun 04 2017

Keywords

Comments

Paths of length zero are not counted here. - Andrew Howroyd, Jun 10 2017

Crossrefs

Extensions

a(5)-a(10) from Andrew Howroyd, Jun 10 2017

A288032 Number of (undirected) paths in the n X n grid graph.

Original entry on oeis.org

0, 12, 322, 14248, 1530196, 436619868, 343715004510, 766012555199052, 4914763477312679808, 91781780911712980966236, 5028368533802124263609489682, 813124448051069045700905179168520
Offset: 1

Views

Author

Eric W. Weisstein, Jun 04 2017

Keywords

Comments

Paths of length zero are not counted here. - Andrew Howroyd, Jun 10 2017

Crossrefs

Main diagonal of A288518.

Extensions

a(6)-a(12) from Andrew Howroyd, Jun 10 2017

A343307 a(n) is the number of self-avoiding paths connecting consecutive corners of an n X n triangular grid.

Original entry on oeis.org

1, 2, 10, 108, 2726, 168724, 25637074, 9454069104, 8461610420420, 18438745892175008, 97929194419509169380, 1267379450261470833222676, 39964658780097197018058705552, 3071011528804416058638501563820092, 575150143830631835000028468717331605240
Offset: 1

Views

Author

Rémy Sigrist, Apr 11 2021

Keywords

Comments

We use unit moves parallel to the triangle edges.

Examples

			For n = 3:
- we have the following paths:
.                         .
.
.                       .   .
.
.                     o---o---o
.
.
.          .              .              .
.
.        o   .          o   o          .   o
.       / \            / \ / \            / \
.      o   o---o      o   o   o      o---o   o
.
.
.          .              .              .
.
.        o---o          o---o          o---o
.       /   /          /     \          \   \
.      o   o---o      o   .   o      o---o   o
.
.
.          o              o              o
.         / \            / \            / \
.        o   o          o   o          o   o
.       /   /          /     \          \   \
.      o   o---o      o   .   o      o---o   o
- so a(3) = 10.
		

Crossrefs

Programs

  • Python
    # See Links section.

Extensions

a(14)-a(15) from Andrew Howroyd, Feb 04 2022

A308144 Number of (undirected) Hamiltonian paths on the triangular grid with n vertices on each side.

Original entry on oeis.org

1, 3, 12, 114, 1968, 66312, 4381020, 578266212, 153350225268, 82409298702462, 90180040305841212, 201800030110625440248, 926548406689594565864346, 8752381854153235620928637604
Offset: 1

Views

Author

Eric W. Weisstein, May 14 2019

Keywords

Crossrefs

Formula

a(n) = A112675(n)/2 for n > 1.

Extensions

a(1) corrected by Andrew Howroyd, Jan 19 2022
Showing 1-4 of 4 results.