cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A320310 (1/4) * number of ways to select 3 distinct points forming a triangle of unsigned area = n/2 from a square of grid points with side length n.

Original entry on oeis.org

1, 8, 23, 82, 114, 416, 373, 1149, 1351, 2598, 2113, 7158, 4094, 9344, 11528, 18243, 11882, 33006, 18603, 48760, 42102, 54312, 40061, 121728, 68115, 105204, 112546, 178322, 101798, 284980, 133229, 300367, 247900, 305062, 295972, 625544, 271864, 475004, 479658, 847208
Offset: 1

Views

Author

Hugo Pfoertner, Oct 23 2018

Keywords

Comments

Permutations of the 3 points are not counted separately.

Crossrefs

Extensions

a(35)-a(40) from Giovanni Resta, Oct 26 2018

A372915 a(n) is the number of distinct triangles with area n whose vertices are points of an n X n grid.

Original entry on oeis.org

0, 0, 2, 4, 9, 10, 25, 22, 38, 49, 56, 56, 111, 71, 119, 141, 153, 126, 249, 166, 244, 299, 279, 244, 463, 288, 361, 489, 517, 373, 677, 436, 626, 719, 620, 665, 1078, 604, 811, 936, 1000, 749, 1444, 842, 1221, 1384, 1173, 1016, 1871, 1261, 1393, 1597, 1566, 1259
Offset: 0

Views

Author

Felix Huber, Jun 02 2024

Keywords

Examples

			See the linked illustration for the term a(4) = 9.
		

Crossrefs

Programs

  • Maple
    A372915:=proc(n)
      local p,q,g,h,u,v,x,y,L,M;
      L:=[];
      for g from 2 to n do
        h:=2*n/g;
        if type(h,integer) then
          for x to n do
            M:=[g,sqrt(x^2+h^2),sqrt((g-x)^2+h^2)];
            M:=sort(M);
            if not member(M,L) then
              L:=[op(L),M];
            fi;
          od;
        fi;
      od;
      for p to n do
        for q from 1 to p do
          g:=sqrt(p^2+q^2);
          h:=2*n/g;
          u:=h/g*q;
          v:=q+h/g*p;
          for x from max(1,ceil(p/q*(v-n)+u)) to min(n,floor(p/q*v+u)) do
            y:=q/p*(u-x)+v;
            if type(y,integer) and x <> p and y <> q then
              M:=[g,sqrt(x^2+(y-q)^2),sqrt((x-p)^2+y^2)];
              M:=sort(M);
              if not member(M,L) then
                L:=[op(L),M];
              fi;
            fi;
          od;
        od;
      od;
      return numelems(L);
    end proc;
    seq(A372915(n),n=0..53);
Showing 1-2 of 2 results.