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

%I A368639 #14 Jan 13 2024 04:45:17
%S A368639 1,3,17,111,757,5321,38131,276913,2031075,15011373,111618559,
%T A368639 834026649,6257264575,47105424671,355648865425,2691925368489,
%U A368639 20420008516447,155197818599687,1181563534890855,9009291052956319,68788955737056469,525876413869285467
%N A368639 Number of lattice paths from (0,0) to (n,n) using steps (i,j) with i,j>=0 and gcd(i,j)=1.
%H A368639 Alois P. Heinz, <a href="/A368639/b368639.txt">Table of n, a(n) for n = 0..400</a>
%F A368639 a(n) = A362242(2n,n).
%F A368639 a(n) mod 2 = 1.
%F A368639 a(n) ~ c * d^n / sqrt(n), where d = 7.83243076186533979978704688382432500791136... and c = 0.4087157525553882018687231317140076547941617894... - _Vaclav Kotesovec_, Jan 13 2024
%e A368639 a(1) = 3: (00)(10)(11), (00)(01)(11), (00)(11).
%p A368639 b:= proc(n, k) option remember; `if`(min(n, k)=0, 1, add(add(
%p A368639       `if`(igcd(i, j)=1, b(n-i, k-j), 0), j=0..k), i=0..n))
%p A368639     end:
%p A368639 a:= n-> b(n$2):
%p A368639 seq(a(n), n=0..21);
%Y A368639 Cf. A362242.
%K A368639 nonn
%O A368639 0,2
%A A368639 _Alois P. Heinz_, Jan 01 2024