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

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

Offset

1,2

Comments

We use unit moves parallel to the triangle edges.

Links

Table of n, a(n) for n=1..15.

Rémy Sigrist, Python program for A343307

Eric Weisstein's World of Mathematics, Triangular Grid Graph

Index entries for sequences related to walks

Example

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.

Prog

(Python) # See Links section.

Crossrefs

Cf. A007764, A112675, A288148, A308144, A343310.

Sequence in context: A003222 A262145 A355209 * A003167 A240625 A062412

Adjacent sequences: A343304 A343305 A343306 * A343308 A343309 A343310

Keyword

nonn,walk,hard

Author

Rémy Sigrist, Apr 11 2021

Extensions

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

Status

approved