OFFSET
1,1
COMMENTS
A trapezoid is a quadrilateral with at least one pair of parallel sides.
Conjecture: in this sequence are only four terms which belong to trapezoids with exactly one pair of parallel sides: a(2) = 18, a(4) = 20, a(6) = 24, a(7) = 30.
For s >= 4, a rhombus with side s and height 4 has a perimeter and area equal to 4s. Without the requirement that the offset between the two bases being integral all multiples of 4 >= 16 would also be included. - Rahid Zaman, Feb 16 2026
LINKS
Felix Huber, Illustration of terms a(1) to a(11)
Eric Weisstein's World of Mathematics,Trapezoid.
Wikipedia, Trapezoid.
EXAMPLE
See attached illustration of the terms a(1) to a(11).
MAPLE
with(NumberTheory):
A374594:=proc(k);
local K, L, S, T, i, a, c, x, y, h, b, d;
L:=map(x->x/2, Divisors(2*k) minus {1, 2});
S:=[];
T:=[];
K:=[];
for i to numelems(L) do
for c to L[i] do
a:=2*L[i]-c;
h:=k/L[i];
x:=0;
while x^2<(k-a-c)^2-h^2 do
if issqr(x^2+h^2) then
d:=isqrt(x^2+h^2);
b:=k-a-c-d;
y:=a-c-x;
if h^2+y^2=b^2 then
S:=[a, b, c, d];
S:=sort(S);
if member(S, T)=false then
T:=[op(T), S];
K:=[op(K), k];
fi;
fi;
fi;
x:=x+1;
od;
od;
od;
if numelems(K)>0 then
return op(K)
fi;
end proc;
seq(A374594(k), k=1..3000);
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Felix Huber, Jul 13 2024
EXTENSIONS
Corrected by Felix Huber, Dec 04 2024
Name clarified and more terms from Rahid Zaman, Feb 16 2026
STATUS
approved
