A368639 Number of lattice paths from (0,0) to (n,n) using steps (i,j) with i,j>=0 and gcd(i,j)=1.

1, 3, 17, 111, 757, 5321, 38131, 276913, 2031075, 15011373, 111618559, 834026649, 6257264575, 47105424671, 355648865425, 2691925368489, 20420008516447, 155197818599687, 1181563534890855, 9009291052956319, 68788955737056469, 525876413869285467

Offset: 0

Author

Alois P. Heinz, Jan 01 2024

Keywords

• nonn

Examples

			a(1) = 3: (00)(10)(11), (00)(01)(11), (00)(11).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A362242.

Programs

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);

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