OFFSET
0,2
COMMENTS
The walks counted are all those directly along and x or y axes, and all walks whose final (|x|,|y|) lattice point are the two legs of a Pythagorean triple.
LINKS
Wikipedia, Self-avoiding walk.
EXAMPLE
a(3) = 12 as, in the first quadrant, there is one 3-step SAW whose end-to-end distance is an integer (1 unit):
.
X---.
|
X---.
.
This can be walked in 8 different ways on a 2D square lattice. There are also the four walks directly along the x and y axes, giving a total of 8 + 4 = 12 walks.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Scott R. Shannon, Jan 12 2023
STATUS
approved