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

Author

Rémy Sigrist, Apr 11 2021

Keywords

• nonn
• walk
• hard

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.
		

Links

• Rémy Sigrist, Python program for A343307
• Eric Weisstein's World of Mathematics, Triangular Grid Graph
• Index entries for sequences related to walks

Crossrefs

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

Programs

Python

# See Links section.

Extensions

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