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A343307
a(n) is the number of self-avoiding paths connecting consecutive corners of an n X n triangular grid.
2
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.
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
KEYWORD
nonn,walk,hard
AUTHOR
Rémy Sigrist, Apr 11 2021
EXTENSIONS
a(14)-a(15) from Andrew Howroyd, Feb 04 2022
STATUS
approved