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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.

%I A368672 #13 Jan 13 2024 04:52:32
%S A368672 1,2,5,14,39,110,307,860,2407,6736,18851,52758,147651,413224,1156469,
%T A368672 3236546,9057955,25350028,70945807,198552344,555678123,1555147480,
%U A368672 4352310421,12180584958,34089170027,95403588336,267001063969,747242000068,2091267346883,5852721227868
%N 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.
%H A368672 Alois P. Heinz, <a href="/A368672/b368672.txt">Table of n, a(n) for n = 0..700</a>
%F A368672 a(n) mod 2 = 1 - (n mod 2) = A059841(n).
%F A368672 a(n) ~ c * d^n, where d = 2.798648023933224047287803536948757710187420348758496337690531870498937575... and c = 0.639525188357518889842205998775477309094300590250850025271938769053628196... - _Vaclav Kotesovec_, Jan 13 2024
%p A368672 b:= proc(n, k) option remember; `if`(min(n, k)=0, 1, add(add(
%p A368672       `if`(igcd(i, j)=1, b(n-i, k-j), 0), j=0..k), i=0..n))
%p A368672     end:
%p A368672 a:= n-> add(b(k, n-k), k=0..n):
%p A368672 seq(a(n), n=0..29);
%Y A368672 Row sums of A362242.
%Y A368672 Cf. A059841.
%K A368672 nonn
%O A368672 0,2
%A A368672 _Alois P. Heinz_, Jan 02 2024