OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..575
J. East and N. C. Ham, Lattice paths and submonoids of Z^2, arXiv:1811.05735 [math.CO], 2018.
N. C. Ham, Implementation of algorithms 1-3 from J. East and N. C. Ham reference above.
Wikipedia, Euclid's orchard
FORMULA
a(n) mod 2 = 1. - Alois P. Heinz, May 13 2019
a(n) ~ c * d^n / sqrt(n), where d = 3.7137893481485186502229788321701955452444... and c = 0.133597878112414800677299372849715598093... - Vaclav Kotesovec, May 24 2019
MAPLE
b:= proc(x, y) option remember; `if`(y=0, 1, add(add(`if`(1=
igcd(h, v), b(sort([x-h, y-v])[]), 0), v=1..y), h=1..x))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30); # Alois P. Heinz, May 12 2019
MATHEMATICA
b[x_, y_] := b[x, y] = If[y == 0, 1, Sum[Sum[If[1 == GCD[h, v], b @@ Sort[{x - h, y - v}], 0], {v, 1, y}], {h, 1, x}]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Feb 29 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Nicholas Ham, May 11 2019
EXTENSIONS
a(16)-a(27) from Alois P. Heinz, May 12 2019
STATUS
approved