A372217 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.

0, 1, 3, 8, 14, 36, 48, 100, 146, 232, 294, 502, 595, 938, 1143, 1433, 1741, 2512, 2826, 3911, 4458, 5319, 6067, 7976, 8728, 10750, 12076, 14194, 15671, 19510, 20669, 25349, 28115, 31716, 34697, 39467, 41894, 49766, 54046, 59948, 63951, 74818, 78216, 90773, 97220

Offset: 0

Author

Felix Huber, Apr 28 2024

Keywords

• nonn

Examples

			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.
		

Links

• Felix Huber, Illustration of the terms a(1) to a(6).

Crossrefs

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

Programs

Maple

S372217:=proc(n);
  local s,x,u,v;
  s:=0;
  if n=1 then return 1 fi;
  for x to n do
    if gcd(x,n)=1 then
      for u from x to n do
        for v from 0 to n do
          if gcd(u,v)=1 and gcd(u-x,n-v)=1 then
            if u=x then s:=s+1;
            fi;
          fi;
        od;
      od;
    fi;
  od;
  return s;
end proc;
A372217:=proc(n)
  local i,a;
  a:=0;
  for i from 0 to n do
    a:=a+S372217(i);
  od;
  return a;
end proc;
seq(A372217(n),n=0..44);