A372217 - OEIS

%I #28 Jun 17 2024 15:24:58

%S 0,1,3,8,14,36,48,100,146,232,294,502,595,938,1143,1433,1741,2512,

%T 2826,3911,4458,5319,6067,7976,8728,10750,12076,14194,15671,19510,

%U 20669,25349,28115,31716,34697,39467,41894,49766,54046,59948,63951,74818,78216,90773,97220

%N a(n) is the number of distinct triangles whose sides do not pass through a grid point and whose vertices are three points of an n X n grid.

%H Felix Huber, <a href="/A372217/a372217.pdf">Illustration of the terms a(1) to a(6)</a>.

%e See the linked illustration for the terms a(1) = 1, a(2) = 3, a(3) = 8, a(4) = 14, a(5) = 36 and a(6) = 48.

%p S372217:=proc(n);

%p   local s,x,u,v;

%p   s:=0;

%p   if n=1 then return 1 fi;

%p   for x to n do

%p     if gcd(x,n)=1 then

%p       for u from x to n do

%p         for v from 0 to n do

%p           if gcd(u,v)=1 and gcd(u-x,n-v)=1 then

%p             if u<n then s:=s+1;

%p             elif v>=x then s:=s+1;

%p             fi;

%p           fi;

%p         od;

%p       od;

%p     fi;

%p   od;

%p   return s;

%p end proc;

%p A372217:=proc(n)

%p   local i,a;

%p   a:=0;

%p   for i from 0 to n do

%p     a:=a+S372217(i);

%p   od;

%p   return a;

%p end proc;

%p seq(A372217(n),n=0..44);

%Y Cf. A115004, A141224, A141255, A320540, A320541, A320544, A372218.

%K nonn

%O 0,3

%A _Felix Huber_, Apr 28 2024