A362242 -id:A362242 - cp's OEIS frontend

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

Alois P. Heinz, Jan 01 2024

nonn

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

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

Cf. A362242.

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);

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

A368672 Total number of lattice paths from (0,0) to (k,n-k) for k=0..n using steps (i,j) with i,j>=0 and gcd(i,j)=1.

Original entry on oeis.org

1, 2, 5, 14, 39, 110, 307, 860, 2407, 6736, 18851, 52758, 147651, 413224, 1156469, 3236546, 9057955, 25350028, 70945807, 198552344, 555678123, 1555147480, 4352310421, 12180584958, 34089170027, 95403588336, 267001063969, 747242000068, 2091267346883, 5852721227868

Offset: 0

Alois P. Heinz, Jan 02 2024

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..700

Row sums of A362242.

Cf. A059841.

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-> add(b(k, n-k), k=0..n):
seq(a(n), n=0..29);

a(n) mod 2 = 1 - (n mod 2) = A059841(n).

a(n) ~ c * d^n, where d = 2.798648023933224047287803536948757710187420348758496337690531870498937575... and c = 0.639525188357518889842205998775477309094300590250850025271938769053628196... - Vaclav Kotesovec, Jan 13 2024

cp's OEIS Frontend

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

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