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A372915
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a(n) is the number of distinct triangles with area n whose vertices are points of an n X n grid.
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3
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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
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listen;
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OFFSET
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0,3
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LINKS
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EXAMPLE
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See the linked illustration for the term a(4) = 9.
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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