A372915 a(n) is the number of distinct triangles with area n whose vertices are points of an n X n grid.
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
Keywords
Examples
See the linked illustration for the term a(4) = 9.
Links
- Felix Huber, Table of n, a(n) for n=0..666
- Felix Huber, Illustration of the term a(4) = 9
Programs
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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);
Comments