A343310 a(n) is the number of bilaterally symmetrical self-avoiding paths connecting consecutive corners of an n X n triangular grid.

1, 2, 4, 12, 50, 264, 2054, 22324, 377704, 9455172, 385118374, 23504746636, 2346325946460, 348814672315896, 84278783653480026, 30255270733134656280, 17646594353716082850430, 15321207204408662854455924, 21654163559101840305705453010, 45620955950222177660249163228084

Offset: 1

Author

Rémy Sigrist, Apr 11 2021

Keywords

• nonn
• walk

Comments

We use unit moves parallel to the triangle edges.

Examples

			For n = 3:
- we have the following bilaterally symmetrical paths:
.        .             .             .             o
.                                                 / \
.      .   .         o   o         o---o         o   o
.                   / \ / \       /     \       /     \
.    o---o---o     o   o   o     o   .   o     o   .   o
- so a(3) = 4.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..25
• Rémy Sigrist, Illustrations of a(5) = 50
• Rémy Sigrist, PARI program for A343310
• Eric Weisstein's World of Mathematics, Triangular Grid Graph
• Index entries for sequences related to walks

Crossrefs

Cf. A343307.

Programs

PARI

See Links section.

Formula

a(n) <= A343307(n).

Extensions

a(12)-a(13) from Martin Ehrenstein, May 02 2021

Terms a(14) and beyond from Andrew Howroyd, Feb 05 2022