login
A368639
Number of lattice paths from (0,0) to (n,n) using steps (i,j) with i,j>=0 and gcd(i,j)=1.
2
1, 3, 17, 111, 757, 5321, 38131, 276913, 2031075, 15011373, 111618559, 834026649, 6257264575, 47105424671, 355648865425, 2691925368489, 20420008516447, 155197818599687, 1181563534890855, 9009291052956319, 68788955737056469, 525876413869285467
OFFSET
0,2
LINKS
FORMULA
a(n) = A362242(2n,n).
a(n) mod 2 = 1.
a(n) ~ c * d^n / sqrt(n), where d = 7.83243076186533979978704688382432500791136... and c = 0.4087157525553882018687231317140076547941617894... - Vaclav Kotesovec, Jan 13 2024
EXAMPLE
a(1) = 3: (00)(10)(11), (00)(01)(11), (00)(11).
MAPLE
b:= proc(n, k) option remember; `if`(min(n, k)=0, 1, add(add(
`if`(igcd(i, j)=1, b(n-i, k-j), 0), j=0..k), i=0..n))
end:
a:= n-> b(n$2):
seq(a(n), n=0..21);
CROSSREFS
Cf. A362242.
Sequence in context: A295808 A215048 A346921 * A119259 A249921 A174404
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 01 2024
STATUS
approved